(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 559070, 15055]*) (*NotebookOutlinePosition[ 582485, 15790]*) (* CellTagsIndexPosition[ 576864, 15610]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["TARCER 1.1", "Title", TextAlignment->Center, CellTags->"T1.1"], Cell[TextData[{ "A ", StyleBox["Mathematica", FontSlant->"Italic"], " program for the reduction of two-loop propagator integrals " }], "Text", TextAlignment->Center], Cell[TextData[{ "Rolf Mertig\n", ButtonBox["Mertig Research & Consulting\n", ButtonData:>{ URL[ "http://www.mertig.com"], None}, ButtonStyle->"Hyperlink"], "and\nRainer Scharf\n", ButtonBox["Universit\[ADoubleDot]t Leipzig", ButtonData:>{ URL[ "http://www.physik.uni-leipzig.de/~scharf/"], None}, ButtonStyle->"Hyperlink"] }], "Text", Editable->False, TextAlignment->Center, CellTags->"T1.2"], Cell["April 16, 1998", "Text", TextAlignment->Center], Cell[TextData[{ "See also: ", ButtonBox["hep-ph/9801383", ButtonData:>{ URL[ "http://xxx.lanl.gov/abs/hep-ph/9801383"], None}, ButtonStyle->"Hyperlink"] }], "Text", Editable->False], Cell[CellGroupData[{ Cell["Table of contents", "Section", CellDingbat->"\[FilledSmallCircle]"], Cell["\<\ This cell can be copied into a separate notebook (e.g. TARCERTOC.nb) which \ has to be saved into the same directory as TARCER.nb.\ \>", "Text"], Cell[TextData[ButtonBox["Preliminaries", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.1.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Usages", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.2.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Creating the tarcerij.mx file", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.2.1.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Prologue (setting of $RankLimit)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.3.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Typesetting rules", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.3.1.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["The Palettes", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.3.2.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["OperatorApply", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.3.3.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MassDerivative", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.3.4.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["TarasovT", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.3.5.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["ApplyTarasovT", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.3.6.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Misc", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.3.7.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Colors", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.3.7.1.1"}, ButtonStyle->"Hyperlink"]], "SmallText"], Cell[TextData[ButtonBox["PQ", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.3.7.2.1"}, ButtonStyle->"Hyperlink"]], "SmallText"], Cell[TextData[ButtonBox["PNQ", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.3.7.3.1"}, ButtonStyle->"Hyperlink"]], "SmallText"], Cell[TextData[ButtonBox["FactorC", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.3.7.4.1"}, ButtonStyle->"Hyperlink"]], "SmallText"], Cell[TextData[ButtonBox["TFI", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.3.7.5.1"}, ButtonStyle->"Hyperlink"]], "SmallText"], Cell[TextData[ButtonBox["TJI", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.3.7.6.1"}, ButtonStyle->"Hyperlink"]], "SmallText"], Cell[TextData[ButtonBox["TBI", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.3.7.7.1"}, ButtonStyle->"Hyperlink"]], "SmallText"], Cell[TextData[ButtonBox["TAI", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.3.7.8.1"}, ButtonStyle->"Hyperlink"]], "SmallText"], Cell[TextData[ButtonBox["Definitions and notation", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.4.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[StyleBox[ButtonBox["ToArgs", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.4.1.1"}, ButtonStyle->"Hyperlink"], FontColor->RGBColor[0.2, 0.6, 1]]], "Text"], Cell[TextData[StyleBox[ButtonBox["Cayley", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.4.2.1"}, ButtonStyle->"Hyperlink"], FontColor->RGBColor[1, 0, 0.4]]], "Text"], Cell[TextData[Cell[BoxData[ FormBox[ ButtonBox[ StyleBox[ RowBox[{ RowBox[{ StyleBox["Cayley", FontColor->RGBColor[1, 0, 0.4]], "[", "i", "]"}], "=", \(\[CapitalDelta]\_i\)}], SingleLetterItalics->False], ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.4.3.1"}, Active->True, Background->GrayLevel[1], ButtonNote->ButtonData], TextForm]]]], "Text"], Cell[TextData[Cell[BoxData[ FormBox[ ButtonBox[ StyleBox[ RowBox[{ RowBox[{ StyleBox["CayleyD", FontColor->RGBColor[1, 0.2, 1]], "[", "i", "]"}], "=", \(\[CapitalDelta]\_i/\[CapitalDelta]\)}], SingleLetterItalics->False], ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.4.4.1"}, Active->True, Background->GrayLevel[1], ButtonNote->ButtonData], TextForm]]]], "Text"], Cell[TextData[ButtonBox["Utility Functions", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.5.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun and friends", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.5.1.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Interchange", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.5.1.1.1"}, ButtonStyle->"Hyperlink"]], "SmallText"], Cell[TextData[ButtonBox["\[Nu]", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.5.2.1"}, ButtonStyle->"Hyperlink"], ButtonBox["explicit", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.5.2.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["TA", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.5.2.1.1"}, ButtonStyle->"Hyperlink"]], "SmallText"], Cell[TextData[ButtonBox["CheckRecursion", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.5.3.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["CheckTVIRecursion", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.5.3.1.1"}, ButtonStyle->"Hyperlink"]], "SmallText"], Cell[TextData[ButtonBox["CheckTJIRecursion", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.5.3.2.1"}, ButtonStyle->"Hyperlink"]], "SmallText"], Cell[TextData[ButtonBox[ "Recurrence Relations Input and Recursion Function Generation", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (35)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.1.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (35)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.2.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[Cell[BoxData[ FormBox[ ButtonBox[ StyleBox[ RowBox[{ FormBox[\(1\^\(+\ \)\), "TraditionalForm"], \(\ \((35 _ 1)\)\)}], SingleLetterItalics->False], ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.2.1.1"}, Active->True, Background->GrayLevel[1], ButtonNote->ButtonData], TraditionalForm]]]], "SmallText"], Cell[TextData[Cell[BoxData[ FormBox[ ButtonBox[ StyleBox[ RowBox[{ FormBox[\(2\^\(+\ \)\), "TraditionalForm"], \(\ \((35 _ 2)\)\)}], SingleLetterItalics->False], ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.2.2.1"}, Active->True, Background->GrayLevel[1], ButtonNote->ButtonData], TraditionalForm]]]], "SmallText"], Cell[TextData[Cell[BoxData[ FormBox[ ButtonBox[ StyleBox[ RowBox[{ FormBox[\(3\^\(+\ \)\), "TraditionalForm"], \(\ \((35 _ 3)\)\)}], SingleLetterItalics->False], ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.2.3.1"}, Active->True, Background->GrayLevel[1], ButtonNote->ButtonData], TraditionalForm]]]], "SmallText"], Cell[TextData[Cell[BoxData[ FormBox[ ButtonBox[ StyleBox[ RowBox[{ FormBox[\(4\^\(+\ \)\), "TraditionalForm"], \(\ \((35 _ 4)\)\)}], SingleLetterItalics->False], ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.2.4.1"}, Active->True, Background->GrayLevel[1], ButtonNote->ButtonData], TraditionalForm]]]], "SmallText"], Cell[TextData[ButtonBox["Input (3501)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.3.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[Cell[BoxData[ FormBox[ ButtonBox[ StyleBox[ RowBox[{\(MakeFun\ \((3501)\)\ \[CapitalDelta] = 0\ \), FormBox[\((p\^2 = m\^2)\), "TraditionalForm"]}], SingleLetterItalics->False], ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.4.1"}, Active->True, Background->GrayLevel[1], ButtonNote->ButtonData], TraditionalForm]]]], "Text"], Cell[TextData[ButtonBox["Input (3502)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.5.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[Cell[BoxData[ FormBox[ ButtonBox[ StyleBox[ RowBox[{\(MakeFun\ \((3502)\)\ \[CapitalDelta] = 0\ \), FormBox[\((p\^2 = m\^2)\), "TraditionalForm"]}], SingleLetterItalics->False], ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.6.1"}, Active->True, Background->GrayLevel[1], ButtonNote->ButtonData], TraditionalForm]]]], "Text"], Cell[TextData[Cell[BoxData[ FormBox[ ButtonBox[ StyleBox[ RowBox[{\(MakeFun\ \((3503)\)\ \[CapitalDelta] = 0\ \), FormBox[\((p\^2 = m\^2)\), "TraditionalForm"]}], SingleLetterItalics->False], ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.7.1"}, Active->True, Background->GrayLevel[1], ButtonNote->ButtonData], TraditionalForm]]]], "Text"], Cell[TextData[Cell[BoxData[ FormBox[ ButtonBox[ StyleBox[ RowBox[{\(MakeFun\ \((3504)\)\ \[CapitalDelta] = 0\ \), FormBox[\((p\^2 = m\^2)\), "TraditionalForm"]}], SingleLetterItalics->False], ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.8.1"}, Active->True, Background->GrayLevel[1], ButtonNote->ButtonData], TraditionalForm]]]], "Text"], Cell[TextData[ButtonBox["Input (41)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.9.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (41)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.10.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (43)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.11.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (44)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.12.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (45)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.13.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (43) and (44)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.14.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (50)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.15.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (51)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.16.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (51)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.17.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (52)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.18.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (52)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.19.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (53)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.20.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (54)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.21.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (54)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.22.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (55)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.23.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (55)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.24.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (56)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.25.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (56)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.26.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (59)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.27.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (59)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.28.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (60)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.29.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (60)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.30.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (61)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.31.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (61)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.32.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (6153)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.33.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (62)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.34.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (62)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.35.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (63)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.36.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (63)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.37.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (6552)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.38.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (6552)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.39.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (6553)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.40.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (66)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.41.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (66)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.42.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (alternative67)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.43.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (67)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.44.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (67)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.45.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (6713)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.46.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (68)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.47.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (68)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.48.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (6813)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.49.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (70)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.50.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (70)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.51.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (71)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.52.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (71)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.53.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (7123)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.54.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (7113)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.55.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (78)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.56.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (78)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.57.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (80)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.58.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (80)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.59.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (81)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.60.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (81)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.61.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (8123)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.62.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (8113)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.63.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (82)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.64.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (82)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.65.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (8213)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.66.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (8212)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.67.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (83)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.68.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (83)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.69.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (87)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.70.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["(88)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.70.1.1"}, ButtonStyle->"Hyperlink"]], "SmallText"], Cell[TextData[ButtonBox["(89)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.70.2.1"}, ButtonStyle->"Hyperlink"]], "SmallText"], Cell[TextData[ButtonBox["MakeFun (87)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.71.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (90)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.72.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (90)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.73.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (91)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.74.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (911)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.75.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (912)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.76.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (913)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.77.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (914)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.78.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (92)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.79.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (93)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.80.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (93)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.81.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (94)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.82.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (94)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.83.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (9401)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.84.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (9402)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.85.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (95)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.86.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (95)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.87.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (96)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.88.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (96)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.89.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (97)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.90.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (97)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.91.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (98)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.92.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (98)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.93.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (99)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.94.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (99)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.95.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (9912)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.96.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (9913)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.97.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (100)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.98.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (100)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.99.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (1002)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.100.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (1003)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.101.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (1004)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.102.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (1005)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.103.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (1006)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.104.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (150)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.105.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (150)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.106.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (151)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.107.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (151)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.108.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (152)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.109.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (152)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.110.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (153)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.111.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (153)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.112.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (200)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.113.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (200)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.114.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (201)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.115.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (202)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.116.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (203)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.117.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (204)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.118.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["MakeFun (205)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.119.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Input (1xxxx)", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.120.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["five -> four", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.121.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["four -> three", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.122.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["three -> two", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.123.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["two -> one", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.6.124.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["TarcerRecurse and TFIRecurse", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.7.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["TFIRecurse", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.7.1.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["T*IS", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.7.2.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["TComment", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.7.3.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["TarcerRecurse", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.7.4.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["TarcerExpand", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.8.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Construct T's", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.9.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["$BasisIntegrals", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.10.1"}, ButtonStyle->"Hyperlink"]], "Text"], Cell[TextData[ButtonBox["Save", ButtonData:>{ FrontEnd`FileName[ {}, "TARCER.nb", CharacterEncoding -> "WindowsANSI"], "T1.9.1"}, ButtonStyle->"Hyperlink"]], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Preliminaries", "Section", CellDingbat->"\[FilledSmallCircle]", CellTags->"T1.1.1"], Cell[TextData[{ "This is free software.\nYou may use it, distribute it, change it, improve \ it, etc..\nIf you have ", StyleBox["Mathematica", FontSlant->"Italic"], " questions, ask them to support@wolfram.com or to your local ", StyleBox["Mathematica", FontSlant->"Italic"], " reseller." }], "SmallText", Editable->False], Cell["\<\ We consider the following type of integrals, where a,b,u,v,r,s,t are \ non-negative integers.\ \>", "Text"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm \`\(TFI[d, p\^2, \[CapitalDelta]p, {a, b}, {u, v, r, s, t}\)\)]], ", ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ FormBox[\({{\[Nu]\_1, m\_1}, {\[Nu]\_2, \), "TraditionalForm"], \(m\_2\)}], "}"}], ",", \({\[Nu]\_3, m\_3}\), ",", \({\[Nu]\_4, m\_4}\), ",", \({\[Nu]\_5, m\_5}\)}], "}"}], "]"}], " ", "="}], " "}], TraditionalForm]]], "\n\n", Cell[BoxData[ \(TraditionalForm\`1\/\[Pi]\^d\)]], "\[Integral] \[Integral] ", Cell[BoxData[ FormBox[ FractionBox[ RowBox[{ FormBox[\(\(d\^d\) k\_1\ \(d\^d\) k\_2\ \(\((\[CapitalDelta]\[CenterDot]k\_1)\)\^a\) \(\((\[CapitalDelta]\[CenterDot]k\_1)\)\^b\) \(\((p\[CenterDot]k\_1)\)\^r\) \((\[CapitalDelta]\[CenterDot]k\_1)\)\^s\), "TraditionalForm"], \(\((k\_1\%2)\)\^u\), \(\((k\_2\%2)\)\^v\), \(\((p\[CenterDot]k\_1)\)\^r\), \(\((p\[CenterDot]k\_2)\)\^s\), \(\((k\_1\[CenterDot]k\_2)\)\^t\)}], \(\(\(\(\(\([k\_1\%2 - m\_1\%2]\)\^\[Nu]\_1\)[k\_2\%2 - m\_2\%2] \^\[Nu]\_2\)[\((k\_1 - p)\)\^2 - m\_3\%2] \^\[Nu]\_3\)[\((k\_2 - p)\)\^2 - m\_4\%2] \^\[Nu]\_4\)[\((k\_1 - k\_2)\)\^2 - m\_5\%2]\^\[Nu]\_5 \)], TraditionalForm]]] }], "Text"], Cell["\<\ Putting the $Post = (#;)&; instruction after Unset[$Post] suppresses all output cells. Putting Unset[$Post] behind $Post=(#:)&; will produce a lot of typsetted reduction formulae.\ \>", "Text"], Cell[BoxData[ \(\(Unset[$Post]; \)\)], "Input"], Cell[BoxData[ \(\($Post\ = \ \((#; )\)&; \)\)], "Input"], Cell["\<\ This determines the directory into which the resulting file tarcer.mx is \ written.\ \>", "Text"], Cell[BoxData[ \(SetDirectory[ ToFileName[ First["\" /. NotebookInformation[InputNotebook[]]]]]\)], "Input"], Cell[TextData[{ "Somehow ", StyleBox["Mathematica", FontSlant->"Italic"], " crashes on my (R.M.) good old NeXTStation if I don't open all cells first \ ...; this opens all cells automatically:" }], "SmallText"], Cell[BoxData[ \(If[$System === "\", SelectionMove[EvaluationNotebook[], All, Notebook]; FrontEndExecute[{ FrontEnd`FrontEndToken[EvaluationNotebook[], "\"]}]]\)], "Input"], Cell[CellGroupData[{ Cell["Creating the tarcerij.mx file", "Subsubsection", CellTags->"T1.2.1.1"], Cell[TextData[{ "Running this notebook will produce a tarcerij.mx file where ij will be \ replaced by \nthe two number set by the variable $RankLimit (default 33). \n\ In the same directory as this notebook which can be loaded into ", StyleBox["Mathematica", FontSlant->"Italic"], " by <"Italic"], "as \nmyshellprompt> math -initfile tarcer33.mx" }], "Text"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Usages", "Section", CellDingbat->"\[FilledSmallCircle]", CellTags->"T1.2.1"], Cell["BeginPackage[\"HighEnergyPhysics`Tarcer`\"];", "Input"], Cell[BoxData[ \(Off[General::spell]; \nOff[General::spell1]; \)], "Input"], Cell[BoxData[ \(\(TarcerRecurse::usage = "\"; \)\)], "Input"], Cell[BoxData[ \(\(TarcerExpand::usage = "\ (4+e), order] or TarcerExpand[epxr, d -> \ (4-e), order] or TarcerExpand[expr, d -> (4 - 2 om)substitutes integrals as \ specified by the option TarcerRules, and does a Laurent expansion in the \ variable around 0 at the right hand side of the second argument (i.e., you \ can use whatever convention you like ...). The same effect as \ TarcerExpand[TarcerRecurse[expr], ...] can be achieved by setting the option \ TarcerRecurse of TarcerExpand to True. TarcerExpand[expr, d -> (4+e)] is \ equivalent to TarcerExpand[expr, d -> (4+e), 0].\>"; \)\)], "Input"], Cell[BoxData[ \(\(TarcerReduce::usage = "\"; \)\)], "Input"], Cell[BoxData[ \(\(Cayley::usage = "\"; \)\)], "Input"], Cell[BoxData[ \(\(Cayleyu::usage = "\"; \)\)], "Input"], Cell[BoxData[ \(\(CayleyD::usage = "\"; \)\)], "Input"], Cell[BoxData[ \(\(PreFactor::usage = "\"; \)\)], "Input"], Cell[BoxData[ \(\(SEpsilon::usage = "\"; \)\)], "Input"], Cell[BoxData[ \(\(TFI::usage = "\"; \)\)], "Input"], Cell[BoxData[ \(\(TFIRecurse::usage = "\"; \)\)], "Input"], Cell[BoxData[ \(\(TVI::usage = "\"; \)\)], "Input"], Cell[BoxData[ \(\(TJI::usage = "\"; \)\)], "Input"], Cell[BoxData[ \(\(TKI::usage = "\"; \)\)], "Input"], Cell[BoxData[ \(\(TBI::usage = "\"; \)\)], "Input"], Cell[BoxData[ \(\(TAI::usage = "\"; \)\)], "Input"], Cell[BoxData[ \(\(TFR::usage = "\"; \)\)], "Input"], Cell[BoxData[ \(\(TVR::usage = "\"; \)\)], "Input"], Cell[BoxData[ \(\(TJR::usage = "\"; \)\)], "Input"], Cell[BoxData[ \(\(TBR::usage = "\"; \)\)], "Input"], Cell[BoxData[ \(\(TAR::usage = "\"; \)\)], "Input"], Cell[BoxData[ \(\($RankLimit::usage = "\<$RankLimit is the list of integers specifying the highest possible \ sums of exponents of scalar products; i.e., {a+b, r+s} means that at most \ (Delta.k1)^a * (Delta.k2)^2 * (p.k1)^r * (p.k2)^s in the numerator will be \ calculated (a,b,r,s have to be non-negative integares). $RankLimit has to be \ set in the TARCER.nb notebook. In the tarcer.mx file this is not possible \ anymore.\>"; \)\)], "Input"], Cell[BoxData[ \(\($TarcerRecursed::usage = "\"; \)\)], "Input"], Cell[BoxData[ \(\($BasisIntegrals::usage = "\<$BasisIntegrals is a list of some basis integrals. It is the default \ setting of TarcerReduce of TarcerExpand.\>"; \)\)], "Input"], Cell[BoxData[ \(\($Comment::usage = "\<$Comment can be set to True or False. If set to False no comments \ are generated.\>"; \)\)], "Input"], Cell[BoxData[ \(\($CommentNotebook::usage = "\<$Comment can be set to True or False. Setting it to True will \ generate a separate notebook (if and only if $Comment is True) where the used \ recursion relations are displayed.\>"; \)\)], "Input"], Cell[BoxData[ \(\(Begin["\<`Private`\>"]; \)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Prologue (setting of $RankLimit)", "Section", CellDingbat->"\[FilledSmallCircle]", CellTags->"T1.3.1"], Cell[TextData[{ "This sets the limit up to which the ", Cell[BoxData[ \(TraditionalForm\`T\)]], "-operators are constructed automatically, i.e., $RankLimit = {a+b, r+s} , \ concerning: ", Cell[BoxData[ \(TraditionalForm\`\(\((\[CapitalDelta]\[CenterDot]k\_1)\)\^a\ \)\)]], Cell[BoxData[ \(TraditionalForm\`\((\[CapitalDelta]\[CenterDot]k\_2)\)\^b\)]], " ", Cell[BoxData[ FormBox[ SuperscriptBox[ RowBox[{"(", FormBox[\(p\[CenterDot]k\_1\), "TraditionalForm"], ")"}], "r"], TraditionalForm]]], Cell[BoxData[ FormBox[ SuperscriptBox[ RowBox[{"(", FormBox[\(p\[CenterDot]k\_2\), "TraditionalForm"], ")"}], "s"], TraditionalForm]]] }], "Text"], Cell[BoxData[ \(\($RankLimit = {2, 3}; \)\)], "Input"], Cell["Check recursion relations by changing False to True here:", "Text"], Cell[BoxData[ \(\($CheckRecursion = False; \)\)], "Input"], Cell["\<\ Change False to True for getting the input palettes for entering new \ recursion relations.\ \>", "Text"], Cell[BoxData[ \(\($PutPalettes = False; \)\)], "Input"], Cell[TextData[{ "Notice: Instead of using shift operators", Cell[BoxData[ FormBox[ RowBox[{ FormBox[ RowBox[{" ", StyleBox[\(1\^+\), FontWeight->"Bold"]}], "TraditionalForm"], ",", StyleBox[\(2\^+\), FontWeight->"Bold"]}], TraditionalForm]]], " etc. the \[Nu]-indices are colored blue; instead of ", Cell[BoxData[ FormBox[ RowBox[{ FormBox[ RowBox[{" ", StyleBox[\(1\^-\), FontWeight->"Bold"]}], "TraditionalForm"], ",", StyleBox[\(2\^-\), FontWeight->"Bold"]}], TraditionalForm]]], " etc. the \[Nu]-indices are colored red." }], "Text"], Cell[CellGroupData[{ Cell["Typesetting rules", "Subsection", CellTags->"T1.3.1.1"], Cell[BoxData[ \(\(atime = AbsoluteTime[]; \)\)], "Input"], Cell[BoxData[ \(SEpsilon /: MakeBoxes[SEpsilon[d_], fmt_] := InterpretationBox@@{ StyleBox[SubscriptBox["\", First[Variables[d]]], FontWeight \[Rule] "\"], SEpsilon[d], Editable \[Rule] False}\)], "Input"], Cell[BoxData[ \(MakeBoxes[SEpsilon[d_]\^n_, fmt_] := InterpretationBox@@{ StyleBox[SubsuperscriptBox["\", First[Variables[d]], n], FontWeight \[Rule] "\"], SEpsilon[d], Editable \[Rule] False}\)], "Input"], Cell[BoxData[ \(PreFactor /: MakeBoxes[PreFactor[d_], fmt_] := InterpretationBox@@{MakeBoxes[d, fmt], PreFactor[d], Editable -> False} \)], "Input"], Cell["\<\ Don't mess with the InterpretationBox's !! (important for the palette and \ OperatorApply).\ \>", "Text"], Cell[BoxData[ \(MakeBoxes[Schiebe[i_, pm_String]\ , fmt_] := InterpretationBox[ StyleBox[SuperscriptBox[i, pm], FontWeight -> "\"], Schiebe[i, pm], Editable -> True]\)], "Input"], Cell[BoxData[ \(\(CayleyD /: MakeBoxes[\(CayleyD[i_Integer]\)[args_], fmt_] := FractionBox[SubscriptBox["\<\[CapitalDelta]\>", \ i], "\<\[CapitalDelta]\>"]; \)\)], "Input"], Cell[BoxData[ \(\(CayleyD /: MakeBoxes[\(CayleyD[i_Integer, j_Integer]\)[args_], fmt_] := FractionBox[SubscriptBox["\<\[CapitalDelta]\>", 10\ i + j], "\<\[CapitalDelta]\>"]; \)\)], "Input"], Cell[BoxData[ \(\(CayleyD /: MakeBoxes[\(CayleyD[i_Integer, j_Integer, k_Integer]\)[args_], fmt_] := FractionBox[SubscriptBox["\<\[CapitalDelta]\>", 100\ \ i + 10 j + k], "\<\[CapitalDelta]\>"]; \)\)], "Input"], Cell[BoxData[ \(\(Cayley /: MakeBoxes[\(Cayley[i_Integer]\)[args_], fmt_] := SubscriptBox["\<\[CapitalDelta]\>", \ i]; \)\)], "Input"], Cell[BoxData[ \(\(Cayley /: MakeBoxes[\(Cayley[i_Integer, j_Integer]\)[args_], fmt_] := SubscriptBox["\<\[CapitalDelta]\>", 10\ i + j]; \)\)], "Input"], Cell[BoxData[ \(\(Cayley /: MakeBoxes[\(Cayley[i_Integer, j_Integer, k_Integer]\)[args_], fmt_] := SubscriptBox["\<\[CapitalDelta]\>", 100\ \ i + 10 j + k]; \)\)], "Input"], Cell[BoxData[ \(\(Cayleyu /: MakeBoxes[\(Cayleyu[i_Integer, j_Integer, k_Integer]\)[args_], fmt_] := SubscriptBox["\", 100\ \ i + 10 j + k]; \)\)], "Input"], Cell["\<\ MakeBoxes[PP, fm_] := InterpretationBox[SuperscriptBox[p, 2], PP]; MakeBoxes[m1^(p_), _] := InterpretationBox[SubsuperscriptBox[m, 1, p], m1^p]; \ MakeBoxes[m2^(p_), _] := InterpretationBox[SubsuperscriptBox[m, 2, p], m2^p]; \ MakeBoxes[m3^(p_), _] := InterpretationBox[SubsuperscriptBox[m, 3, p], m3^p]; \ MakeBoxes[m4^(p_), _] := InterpretationBox[SubsuperscriptBox[m, 4, p], m4^p]; \ MakeBoxes[m5^(p_), _] := InterpretationBox[SubsuperscriptBox[m, 5, p], m5^p]; \ m6 = Sqrt[PP]; \ \>", "Input"], Cell[BoxData[ \(MakeBoxes[m1, \ _]\ := \ \n\ \ \ InterpretationBox[SubscriptBox[\n\ \ \ \ \ m, \ 1], \ m1]; \ \n\ \ MakeBoxes[m2, \ _]\ := \ \n\ \ \ InterpretationBox[SubscriptBox[\n\ \ \ \ \ m, \ 2], \ m2]; \ \n\ \ MakeBoxes[m3, \ _]\ := \ \n\ \ \ InterpretationBox[SubscriptBox[\n\ \ \ \ \ m, \ 3], \ m3]; \ \n\ \ MakeBoxes[m4, \ _]\ := \ \n\ \ \ InterpretationBox[SubscriptBox[\n\ \ \ \ \ m, \ 4], \ m4]; \ \n\ \ MakeBoxes[m5, \ _]\ := \ \n\ \ \ InterpretationBox[SubscriptBox[\n\ \ \ \ \ m, \ 5], \ m5]; \)], "Input"], Cell[BoxData[ \(mbt[z_] := ToBoxes[z, TraditionalForm]; \n redblue[z_ /; Head[z] =!= Plus] := mbt[z]; \n redblue[z_\ - 1] := StyleBox[mbt[z], FontColor -> RGBColor[1, \ 0, \ 0]]; \n redblue[z_Subscript\ - 2] := StyleBox[SubscriptBox[OverscriptBox[z[\([1]\)], "\<_\>"], z[\([2]\)]], FontColor -> RGBColor[1, \ 0, \ 0]]; \n redblue[z_\ - 2] := StyleBox[OverscriptBox[mbt[z], "\<_\>"], FontColor -> RGBColor[1, \ 0, \ 0]]; \n redblue[z_\ - 3] := StyleBox[UnderscriptBox[OverscriptBox[mbt[z], "\<_\>"], "\<_\>"], FontColor -> RGBColor[1, \ 0, \ 0]]; \n redblue[z_\ + 1] := StyleBox[mbt[z], FontColor -> RGBColor[0, \ 0, \ 1]]; \n redblue[z_\ + 2] := StyleBox[OverscriptBox[mbt[z], "\<_\>"], FontColor -> RGBColor[0, \ 0, \ 1]]; \n redblue[z_Subscript\ + 2] := StyleBox[SubscriptBox[OverscriptBox[z[\([1]\)], "\<_\>"], z[\([2]\)]], FontColor -> RGBColor[0, \ 0, \ 1]]; \)], "Input"], Cell[BoxData[ \(\(TFI /: MakeBoxes[TFI[d_, pp_, {ur__}, {den__}], fmt_] := \n\t \((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>", "\< \>", ur}]], \n\t\tTFI[d, pp, {ur}, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)\)], "Input"], Cell[BoxData[ \(\(TFI /: MakeBoxes[TFI[d_, pp_, dp_, any__, {den__}], fmt_] := \n\t \(\((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>", "\< \>", Apply[Sequence, Flatten[{any}]]}]], \n\t\t TFI[d, pp, dp, any, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]\) /; Head[dp] =!= List; \)\)], "Input"], Cell[BoxData[ \(\(TFI /: MakeBoxes[TFI[dpp__, {den__}], fmt_] := \n\t \((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[First[{dpp}], TraditionalForm], "\<)\>"}]], \n\t\tTFI[dpp, {den}], Editable -> True}) \) /; MemberQ[{StandardForm, TraditionalForm}, fmt] && Head[Last[{dpp}]] =!= List; \)\)], "Input"], Cell[BoxData[ \(\(TVI /: MakeBoxes[TVI[dpp__, {den__}], fmt_] := \n \((\t\((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[{dpp}[\([1]\)], TraditionalForm], "\<)\>"}]], \n\t\(Hold[TVI]\)[dpp, {den}], Editable -> True})\) /. Hold[TVI] -> TVI)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt] && Head[Last[{dpp}]] =!= List; \)\)], "Input"], Cell[BoxData[ \({TVI[d, {\[Alpha], \[Beta], \[Gamma], \[Delta]}], TVI[d, {\[Alpha] + 1, \[Beta], \[Gamma], \[Delta]}], TVI[d, {\[Alpha] - 1, \[Beta], \[Gamma], \[Delta]}]}\)], "Input"], Cell[BoxData[ \(TJI /: MakeBoxes[TJI[d_, 0, {den__}], fmt_] := \t \((\n\((\((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]], \n\t\t\(Hold[TJI]\)[d, 0, {den}], Editable -> True})\) /. Hold[TJI] -> TJI)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]\n\t)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]\)], "Input"], Cell[BoxData[ \(TJI /: MakeBoxes[TJI[dpp__, {den__}], fmt_] := \t \((\((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[{dpp}[\([1]\)], TraditionalForm], "\<)\>"}]], \n\t\t\(Hold[TJI]\)[dpp, {den}], Editable -> True})\) /. Hold[TJI] -> TJI)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]\)], "Input"], Cell[BoxData[ \(\(TKI /: MakeBoxes[TKI[d_, pp___, {den__}], fmt_] := \n\t \((SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]])\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)\)], "Input"], Cell[BoxData[ \(TKI /: MakeBoxes[TKI[dpp__, {den__}], fmt_] := \t \((\((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[{dpp}[\([1]\)], TraditionalForm], "\<)\>"}]], \n\t\t\(Hold[TKI]\)[dpp, {den}], Editable -> True})\) /. Hold[TKI] -> TKI)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]\)], "Input"], Cell[BoxData[ \({TKI[d, {\[Alpha], \[Beta], \[Gamma]}], TKI[d, {\[Alpha] + 1, \[Beta], \[Gamma]}], TKI[d, {\[Alpha] - 1, \[Beta], \[Gamma]}]}\)], "Input"], Cell[BoxData[ \(\(TBI /: MakeBoxes[TBI[d_, pp___, {den__}], fmt_] := \n\t \((SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]])\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)\)], "Input"], Cell[BoxData[ \(\(TBI /: MakeBoxes[TBI[d_, pp___, {den__}], fmt_] := \n\t \((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]], \n\t \tTBI[d, pp, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)\)], "Input"], Cell[BoxData[ \({TBI[d, {\[Alpha], \[Beta]}], TBI[d, {\[Alpha] + 1, \[Beta]}], TBI[d, {\[Alpha] - 1, \[Beta]}]}\)], "Input"], Cell[BoxData[ \(\(TAI /: MakeBoxes[TAI[d_, pp___, {den__}], fmt_] := \n\t \((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]], \n\t \tTAI[d, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)\)], "Input"], Cell[BoxData[ \({TAI[d, {\[Alpha]}], TAI[d, {\[Alpha] + 1}], TAI[d, {\[Alpha] - 1}]} \)], "Input"], Cell["\<\ T*IC are just like T*I , but used only for commentary in the recursion (TComment).\ \>", "Text"], Cell[BoxData[ \(\(TFIC /: MakeBoxes[TFIC[d_, pp_, {0, 0, i_, 0, 0}, {den__}], fmt_] := \n\t\((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>", "\< \>", i, "\<0\>"}]], \n\t\t TFIC[d, pp, {0, 0, i, 0, 0}, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)\)], "Input"], Cell[BoxData[ \(\(TFIC /: MakeBoxes[TFIC[d_, pp_, {0, 0, 0, i_, 0}, {den__}], fmt_] := \n\t\((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>", "\< \>", "\<0\>", i}]], \n\t\t TFIC[d, pp, {0, 0, 0, i, 0}, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)\)], "Input"], Cell[BoxData[ \(\(TFIC /: MakeBoxes[TFIC[dpp__, {den__}], fmt_] := \n\t \((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[First[{dpp}], TraditionalForm], "\<)\>"}]], \n\t\tTFIC[dpp, {den}], Editable -> True}) \) /; MemberQ[{StandardForm, TraditionalForm}, fmt] && Head[Last[{dpp}]] =!= List; \)\)], "Input"], Cell[BoxData[ \(\(TVIC /: MakeBoxes[TVIC[dpp__, {den__}], fmt_] := \n \((\t\((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[{dpp}[\([1]\)], TraditionalForm], "\<)\>"}]], \n\t\(Hold[TVIC]\)[dpp, {den}], Editable -> True})\) /. Hold[TVIC] -> TVIC)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt] && Head[Last[{dpp}]] =!= List; \)\)], "Input"], Cell[BoxData[ \(TJIC /: MakeBoxes[TJIC[d_, 0, {den__}], fmt_] := \t \((\n\((\((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]], \n\t\t\(Hold[TJIC]\)[d, 0, {den}], Editable -> True})\) /. Hold[TJIC] -> TJIC)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]\n\t)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]\)], "Input"], Cell[BoxData[ \(TJIC /: MakeBoxes[TJIC[dpp__, {den__}], fmt_] := \t \((\((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[{dpp}[\([1]\)], TraditionalForm], "\<)\>"}]], \n\t\t\(Hold[TJIC]\)[dpp, {den}], Editable -> True})\) /. Hold[TJIC] -> TJIC)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]\)], "Input"], Cell[BoxData[ \(\(TBIC /: MakeBoxes[TBIC[d_, pp___, {den__}], fmt_] := \n\t \((SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]])\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)\)], "Input"], Cell[BoxData[ \(\(TBIC /: MakeBoxes[TBIC[d_, pp___, {den__}], fmt_] := \n\t \((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]], \n\t \tTBIC[d, pp, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)\)], "Input"], Cell[BoxData[ \(\(TAIC /: MakeBoxes[TAIC[d_, pp___, {den__}], fmt_] := \n\t \((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]], \n\t \tTAIC[d, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)\)], "Input"], Cell[BoxData[ \(\(TFR /: MakeBoxes[TFR[d_, pp_, {0, 0, i_, 0, 0}, {den__}], fmt_] := \n \t\((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>", "\< \>", i, "\<0\>"}]], \n\t\t TFR[d, pp, {0, 0, i, 0, 0}, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)\)], "Input"], Cell[BoxData[ \(\(TFR /: MakeBoxes[TFR[d_, pp_, {0, 0, 0, i_, 0}, {den__}], fmt_] := \n \t\((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>", "\< \>", "\<0\>", i}]], \n\t\t TFR[d, pp, {0, 0, 0, i, 0}, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)\)], "Input"], Cell[BoxData[ \(\(TFR /: MakeBoxes[TFR[dpp__, {den__}], fmt_] := \n\t \((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[First[{dpp}], TraditionalForm], "\<)\>"}]], \n\t\tTFR[dpp, {den}], Editable -> True}) \) /; MemberQ[{StandardForm, TraditionalForm}, fmt] && Head[Last[{dpp}]] =!= List; \)\)], "Input"], Cell[BoxData[ \(\(TVR /: MakeBoxes[TVR[dpp__, {den__}], fmt_] := \n \((\t\((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[{dpp}[\([1]\)], TraditionalForm], "\<)\>"}]], \n\t\(Hold[TVR]\)[dpp, {den}], Editable -> True})\) /. Hold[TVR] -> TVR)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt] && Head[Last[{dpp}]] =!= List; \)\)], "Input"], Cell[BoxData[ \(TJR /: MakeBoxes[TJR[d_, 0, {den__}], fmt_] := \t \((\n\((\((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]], \n\t\t\(Hold[TJR]\)[d, 0, {den}], Editable -> True})\) /. Hold[TJR] -> TJR)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]\n\t)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]\)], "Input"], Cell[BoxData[ \(TJR /: MakeBoxes[TJR[dpp__, {den__}], fmt_] := \t \((\((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[{dpp}[\([1]\)], TraditionalForm], "\<)\>"}]], \n\t\t\(Hold[TJR]\)[dpp, {den}], Editable -> True})\) /. Hold[TJR] -> TJR)\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]\)], "Input"], Cell[BoxData[ \(\(TBR /: MakeBoxes[TBR[d_, pp___, {den__}], fmt_] := \n\t \((SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]])\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)\)], "Input"], Cell[BoxData[ \(\(TBR /: MakeBoxes[TBR[d_, pp___, {den__}], fmt_] := \n\t \((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]], \n\t \tTBR[d, pp, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)\)], "Input"], Cell[BoxData[ \(\(TAR /: MakeBoxes[TAR[d_, pp___, {den__}], fmt_] := \n\t \((InterpretationBox@@{ SubsuperscriptBox[ StyleBox["\", SingleLetterItalics -> False, FontWeight -> "\"], RowBox@@{\((redblue/@{den})\)}, RowBox[{"\<(\>", ToBoxes[d, TraditionalForm], "\<)\>"}]], \n\t \tTAR[d, {den}], Editable -> True})\) /; MemberQ[{StandardForm, TraditionalForm}, fmt]; \)\)], "Input"], Cell[BoxData[ \(n1 /: MakeBoxes[n1, TraditionalForm] := SubscriptBox["\<\[Nu]\>", 1]; \n n2 /: MakeBoxes[n2, TraditionalForm] := SubscriptBox["\<\[Nu]\>", 2]; \n n3 /: MakeBoxes[n3, TraditionalForm] := SubscriptBox["\<\[Nu]\>", 3]; \n n4 /: MakeBoxes[n4, TraditionalForm] := SubscriptBox["\<\[Nu]\>", 4]; \n n5 /: MakeBoxes[n5, TraditionalForm] := SubscriptBox["\<\[Nu]\>", 5]; \)], "Input"], Cell[BoxData[ \(MakeBoxes[ParD[i_]^j_, TraditionalForm] := SubsuperscriptBox["\<\[PartialD]\>", i, j]; \n MakeBoxes[ParD[i_], TraditionalForm] ^= SubscriptBox["\<\[PartialD]\>", i]; \n MakeBoxes[DPlus, TraditionalForm] := StyleBox[SuperscriptBox["\", "\<+\>"], FontWeight -> "\", \n \tSingleLetterItalics -> False]; \)], "Input"], Cell[BoxData[ \(MakeBoxes[TpD[_, b_], TraditionalForm] := MakeBoxes[b, TraditionalForm]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["The Palettes", "Subsection", CellTags->"T1.3.2.1"], Cell[BoxData[ \(\(If[$PutPalettes === True, \n\t tobut[a_]\ := \ ButtonBox[ToBoxes[a, StandardForm], \ ButtonStyle -> "\"]; \n \ If[Head[pal1] === NotebookObject, \n\tNotebookClose[pal1]]; \n\t pal1 = NotebookPut[ Notebook[{ Cell[BoxData[ GridBox[\n\t\t\t\t\t\t\t Join[Transpose@{\n\t\t\t\t\t\t\t\t\t Table[tobut@\(m\_j\^2\), {j, 5}], \n\t\t\t\t\t\t\t\t \tTable[tobut@\[Nu]\_j, {j, 5}], \n\t\t\t\t\t\t\t\t \tTable[tobut@Schiebe[i, "\<+\>"], {i, 5}], \n\t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Table[tobut@Schiebe[i, "\<-\>"], {i, 5}]}, \n\t\t\t \t\t\t\t{\t tobut/@{PP, \[CapitalDelta]\_\[Placeholder], u\_\[Placeholder], \[ScriptCapitalC]\ }}\n\t\t\t\t \t\t\t], RowSpacings -> 0, \n\ \ \ \ \ \ ColumnSpacings -> 0]], NotebookDefault]}, \n\t Editable -> True, \nWindowToolbars -> {}, \n WindowSize -> {Fit, \ Fit}, \n WindowMargins -> {{0, \ Automatic}, \ {0, Automatic}}, \n WindowFrame -> "\", \nWindowElements -> {}, \n WindowFrameElements -> "\", \n WindowClickSelect -> False, \n ScrollingOptions -> {"\" -> True}, \n ShowCellBracket -> False, \n CellMargins -> {{0, \ 0}, \ {0, \ 0}}, \nActive -> True, \n CellOpen -> True, \nShowCellLabel -> False, \n ShowCellTags -> False, \nImageMargins -> {{0, \ 0}, \ {0, \ 0}}, \nMagnification -> 2, Visible -> True]]; \n SetOptions[pal1, WindowMargins -> {{0, Automatic}, {Automatic, 0}}]; \n SetOptions[pal1, Visible -> True, WindowSize -> {Fit, Fit}]; \n\ If[Head[pal2] === NotebookObject, \n\tNotebookClose[pal2]]; \n\t pal2 = NotebookPut[ Notebook[{ Cell[BoxData[ GridBox[\n\t\t\t\t\t\t\t JJJ = Join[{ tobut/@{ TFI[d + 2, {\[Nu]\_1, \[Nu]\_2, \[Nu]\_3, \[Nu]\_4, \[Nu]\_5}], TVI[d + 2, {\[Nu]\_1, \[Nu]\_2, \[Nu]\_3, \[Nu]\_4}], TJI[d + 2, {\[Nu]\_1, \[Nu]\_2, \[Nu]\_3}], TKI[d, {\[Nu]\_1, \[Nu]\_2, \[Nu]\_3}], TBI[d, {\[Nu]\_1, \[Nu]\_2}], TAI[d, {\[Nu]\_1}]}}, \n\t\t\t\t\t\t\t \t{tobut/@{ TFI[d, {\[Nu]\_1, \[Nu]\_2, \[Nu]\_3, \[Nu]\_4, \[Nu]\_5}], TVI[d, {\[Nu]\_1, \[Nu]\_2, \[Nu]\_3, \[Nu]\_4}], TJI[d, {\[Nu]\_1, \[Nu]\_2, \[Nu]\_3}], TKI[d - 2, {\[Nu]\_1, \[Nu]\_2, \[Nu]\_3}], TBI[d - 2, {\[Nu]\_1, \[Nu]\_2}], TAI[d - 2, {\[Nu]\_1}]}}\n\t\t\t\t\t\t\t], RowSpacings -> 0, \n\ \ \ \ \ \ ColumnSpacings -> 0]], NotebookDefault]}, \n\tEditable -> True, \n WindowToolbars -> {}, \nWindowSize -> {FitAll, \ FitAll}, \n WindowMargins -> {{0, Automatic}, \ {0, Automatic}}, \n WindowFrame -> "\", \nWindowElements -> {}, \n WindowFrameElements -> "\", \n WindowClickSelect -> False, \n ScrollingOptions -> {"\" -> True}, \n ShowCellBracket -> False, \nCellMargins -> {{0, 0}, \ {0, 0}}, \n Active -> True, \nCellOpen -> True, \nShowCellLabel -> False, \n ShowCellTags -> False, \nImageMargins -> {{0, 0}, \ {0, \ 0}}, \n Magnification -> 2, Visible -> True]]; \n SetOptions[pal2, WindowMargins -> {{Automatic, 15}, {Automatic, 4}}]; \n SetOptions[pal2, Visible -> True, WindowSize -> {Fit, Fit}]; \n\t SetOptions[pal2, WindowSize -> {Fit, Fit}]\n\t]; \)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["OperatorApply", "Subsection", CellTags->"T1.3.3.1"], Cell[BoxData[ \(\(OperatorApplyF[x_ == y_] := Block[{sch}, \n\t\t sch\ = \ { Schiebe[i_, "\<+\>"]\^ni_. \ TFI[d_, {n15__}] :> \n\t\t\t\t\t TFI[d, ReplacePart[{n15}, {n15}[\([i]\)] + ni, i]], \n\t\t\t\t Schiebe[i_, "\<-\>"]\^ni_. \ TFI[d_, {n15__}] :> \n\t\t\t\t\t TFI[d, ReplacePart[{n15}, {n15}[\([i]\)] - ni, i]]\n\t\t\t}; Map[Collect[Expand[#] //. sch, TFI[__], Factor]&, \n\t\t\tx == y]]; \)\)], "Input"], Cell[BoxData[ \(\(OperatorApplyV[x_ == y_] := Block[{sch}, \n\t\t sch\ = \ { Schiebe[i_, "\<+\>"]\^ni_. \ TVI[d_, {n15__}] :> \n\t\t\t\t\t TVI[d, ReplacePart[{n15}, {n15}[\([i]\)] + ni, i]], \n\t\t\t\t Schiebe[i_, "\<-\>"]\^ni_. \ TVI[d_, {n15__}] :> \n\t\t\t\t\t TVI[d, ReplacePart[{n15}, {n15}[\([i]\)] - ni, i]]\n\t\t\t}; Map[Collect[Expand[#] //. sch, TVI[__], Factor]&, \n\t\t\tx == y]]; \)\)], "Input"], Cell[BoxData[ \(\(OperatorApplyJ[x_ == y_] := Block[{sch}, \n\t\t sch\ = \ { Schiebe[i_, "\<+\>"]\^ni_. \ TJI[d_, {n15__}] :> \n\t\t\t\t\t TJI[d, ReplacePart[{n15}, {n15}[\([i]\)] + ni, i]], \n\t\t\t\t Schiebe[i_, "\<-\>"]\^ni_. \ TJI[d_, {n15__}] :> \n\t\t\t\t\t TJI[d, ReplacePart[{n15}, {n15}[\([i]\)] - ni, i]]\n\t\t\t}; Map[Collect[Expand[#] //. sch, TJI[__], Factor]&, \n\t\t\tx == y]]; \)\)], "Input"], Cell[BoxData[ \(\(OperatorApplyK[x_ == y_] := Block[{sch}, \n\t\t sch\ = \ { Schiebe[i_, "\<+\>"]\^ni_. \ TKI[d_, {n15__}] :> \n\t\t\t\t\t TKI[d, ReplacePart[{n15}, {n15}[\([i]\)] + ni, i]], \n\t\t\t\t Schiebe[i_, "\<-\>"]\^ni_. \ TKI[d_, {n15__}] :> \n\t\t\t\t\t TKI[d, ReplacePart[{n15}, {n15}[\([i]\)] - ni, i]]\n\t\t\t}; Map[Collect[Expand[#] //. sch, TKI[__], Factor]&, \n\t\t\tx == y]]; \)\)], "Input"], Cell[BoxData[ \(\(OperatorApplyK[x_ == y_] := Block[{sch}, \n\t\t sch\ = \ { Schiebe[i_, "\<+\>"]\^ni_. \ TKI[d_, {n15__}] :> \n\t\t\t\t\t TKI[d, ReplacePart[{n15}, {n15}[\([i]\)] + ni, i]], \n\t\t\t\t Schiebe[i_, "\<-\>"]\^ni_. \ TKI[d_, {n15__}] :> \n\t\t\t\t\t TKI[d, ReplacePart[{n15}, {n15}[\([i]\)] - ni, i]]\n\t\t\t}; Map[Collect[Expand[#] //. sch, TKI[__], Factor]&, \n\t\t\tx == y]]; \)\)], "Input"], Cell[BoxData[ \(\(OperatorApplyB[x_ == y_] := Block[{sch}, \n\t\t sch\ = \ { Schiebe[i_, "\<+\>"]\^ni_. \ TBI[d_, {n15__}] :> \n\t\t\t\t\t TBI[d, ReplacePart[{n15}, {n15}[\([i]\)] + ni, i]], \n\t\t\t\t Schiebe[i_, "\<-\>"]\^ni_. \ TBI[d_, {n15__}] :> \n\t\t\t\t\t TBI[d, ReplacePart[{n15}, {n15}[\([i]\)] - ni, i]]\n\t\t\t}; Map[Collect[Expand[#] //. sch, TBI[__], Factor]&, \n\t\t\tx == y]]; \)\)], "Input"], Cell[BoxData[ \(\(OperatorApplyA[x_ == y_] := Block[{sch}, \n\t\t sch\ = \ { Schiebe[i_, "\<+\>"]\^ni_. \ TAI[d_, {n15__}] :> \n\t\t\t\t\t TAI[d, ReplacePart[{n15}, {n15}[\([i]\)] + ni, i]], \n\t\t\t\t Schiebe[i_, "\<-\>"]\^ni_. \ TAI[d_, {n15__}] :> \n\t\t\t\t\t TAI[d, ReplacePart[{n15}, {n15}[\([i]\)] - ni, i]]\n\t\t\t}; Map[Collect[Expand[#] //. sch, TAI[__], Factor]&, \n\t\t\tx == y]]; \)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MassDerivative", "Subsection", CellTags->"T1.3.4.1"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ \(MassDerivative[ STLI[any__, {\n\ \ \ \ \ \ \ {al_, m1_}, {be_, m2_}, {ga_, m3_}, {de_, m4_}, {ep_, m5_}}], {{0, d1_}, {0, d2_}, \ {0, d3_}, \ {0, d4_}, \ {0, d5_}}]\), StyleBox[" ", FontWeight->"Plain"], StyleBox[":=", FontWeight->"Plain"], "\n", \(\((\ \(Pochhammer[al, d1]\ Pochhammer[be, d2]\ Pochhammer[ga, d3]\)*\n\ \ Pochhammer[de, d4]\ Pochhammer[ep, d5]\ )\)\ *\n\ STLI[any, {{al + d1, m1}, \ {be + d2, m2}, \ {ga + d3, m3}, \ {de + d4, m4}, \ {ep + d5, m5}}]\)}], ";"}], "\n"}]], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["TarasovT", "Subsection", CellTags->"T1.3.5.1"], Cell[BoxData[ \(\(TarasovT[abrs__, \ qq_ /; Head[qq] =!= List]\ := \ TarasovT[abrs, qq, {"\", "\", "\", "\", "\"}]\n\t \)\)], "Input"], Cell[BoxData[ \(\(TarasovT[r_, \ s_, \ qq_, \ {alp1_, alp2_, \ alp3_, alp4_, alp5_}] \ := \nBlock[{\ al1, al2, al3, al4, al5, alrul, new, Q1, Q11, Q12, Q2, Q22}, \n\ If[alp1\ === \ 0, \ al1\ = \ 0]; \ If[alp2\ === \ 0, \ al2\ = \ 0]; \n\ If[alp3\ === \ 0, \ al3\ = \ 0]; \n If[alp4\ === \ 0, \ al4\ = \ 0]; \ If[alp5\ === \ 0, \ al5\ = \ 0]; \n\ alrul\ = \ Select[{al1 :> I\ ParD[1], \ al2 :> I\ ParD[2], \ al3 :> I\ ParD[3], \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ al4 :> I\ ParD[4], \ al5 :> I\ ParD[5]}, \ \(! MatchQ[#, \ 0 :> _]\)&]; \n\ Q1\ = \ al3\ al5\ + \ al4\ al5\ + \ al2\ al3\ + \ al3\ al4; \n\ Q2\ = \ al4\ al5\ + \ al3\ al5\ + \ al1\ al4\ + \ al3\ al4; \n\ Q11\ = 1/\((\(-4\))\)\ \((\ al2\ + \ al4\ + \ al5\ )\); \n\ Q22\ = 1/\((\(-4\))\)\ \((\ al1\ + \ al3\ + \ al5\ )\); \n\ Q12\ = 1/\((\(-2\))\)\ al5; \n\t\t new = \n\ I^\((\(-r\) - s)\) \((\ D[\ Exp[\ I\ qq\ \((\n\ \ \ \ be1\ Q1\ + \ be2\ Q2\ + be1^2\ Q11\ + be2^2\ Q22\ + \ be1\ be2\ Q12\n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ )\)\ rho \ ], {be1, r}, {be2, s}\n\t\t\t\t]\ )\) /. \n\ \((\ Join[alrul, \ {be1\ :> \ 0, be2\ :> \ 0, \ rho\ :> \ \(-Pi^2\)/Pi^2\ DPlus\ }])\); Map[\((Select[#, \((FreeQ[#, ParD] && FreeQ[#, DPlus])\)&]\ TpD[qq, Select[#, \((\(! \((FreeQ[#, ParD] && FreeQ[#, DPlus])\)\))\)&]]) \)&, \((Expand[new, ParD] + \ dum1\ dum2)\)\n\t\t] /. { dum1 :> 0, dum2 :> 0}\n\t\t]; \)\)], "Input"], Cell[BoxData[ \(\(\nTarasovT[r_, \ s_, \ pp_, \ dp_ /; Head[dp] =!= List]\ := \ TarasovT[r, s, pp, dp, {"\", "\", "\", "\", "\"}] \)\)], "Input"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\((\[CapitalDelta]\ q\_1)\)\^a\)]], Cell[BoxData[ \(TraditionalForm\`\((\[CapitalDelta]\ q\_2)\)\^b\)]], Cell[BoxData[ \(TraditionalForm\`\((p\ q\_1)\)\^r\)]], Cell[BoxData[ \(TraditionalForm\`\((p\ q\_2)\)\^s\)]] }], "Text"], Cell[BoxData[ \(\(\n\(TarasovT[a_, b_, r_, s_, pp_, dp_, {alp1_, alp2_, alp3_, alp4_, alp5_}] := Block[{al1, al2, al3, al4, al5, alrul, new, Q1, Q11, Q12, Q2, Q22}, If[alp1 === 0, al1 = 0]; If[alp2 === 0, al2 = 0]; If[alp3 === 0, al3 = 0]; If[alp4 === 0, al4 = 0]; If[alp5 === 0, al5 = 0]; alrul = Select[{al1 \[RuleDelayed] I\ ParD[1], al2 \[RuleDelayed] I\ ParD[2], al3 \[RuleDelayed] I\ ParD[3], al4 \[RuleDelayed] I\ ParD[4], al5 \[RuleDelayed] I\ ParD[5]}, \(\[InvisibleSpace]\(! \((MatchQ[#1, 0 \[RuleDelayed] _])\)\)\)&]; Q1 = al3\ al5 + al4\ al5 + al2\ al3 + al3\ al4; Q2 = al4\ al5 + al3\ al5 + al1\ al4 + al3\ al4; Q11 = \(-\(1\/4\)\)\ \((al2 + al4 + al5)\); Q22 = \(-\(1\/4\)\)\ \((al1 + al3 + al5)\); Q12 = \(-\(al5\/2\)\); new = I\^\(\(-r\) - s - a - b\)\ \[PartialD]\_\({be1, r}, {be2, s}, {ga1, a}, {ga2, b}\)Exp[ I\ \((\((be1\ pp + ga1\ dp)\)\ Q1 + \((be2\ pp + ga2\ dp)\)\ Q2 + be1\ \((be1\ pp + 2\ ga1\ dp)\)\ Q11 + be2\ \((be2\ pp + 2\ ga2\ dp)\)\ Q22 + \((be1\ be2\ pp + \((be1\ ga2 + be2\ ga1)\)\ dp)\)\ Q12)\)\ rho] /. Join[alrul, {be1 \[RuleDelayed] 0, be2 \[RuleDelayed] 0, ga1 :> 0, ga2 :> 0, rho \[RuleDelayed] \(-\(\(\[Pi]\^2\ DPlus\)\/\[Pi]\^2\)\)}]; \((Select[#1, FreeQ[#1, ParD] && FreeQ[#1, DPlus]&]\ TpD[pp, Select[#1, \(\[InvisibleSpace]\(! \((FreeQ[#1, ParD] && FreeQ[#1, DPlus])\)\)\)&]]&) \)/@\((Expand[new] + dum1\ dum2)\) /. {dum1 \[RuleDelayed] 0, dum2 \[RuleDelayed] 0}]; \)\)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["ApplyTarasovT", "Subsection", CellTags->"T1.3.6.1"], Cell[BoxData[ \(ApplyTarasovT[tij_, \ exp_] := Block[{dumpt}, \n\t\tdump = Product[ParD[j]^dummy, {j, 5}]; \n\t\t Expand[tij\ exp] /. \n \((STLI[de_, pp_, pe__List]\ TpD[tpp_, DPlus^i_. \ t_])\) :> \n\t MassDerivative[STLI[\ de /. de :> \((de\ + \ 2\ i)\), pp, pe], \n \t\t\t\t\t\t\t \(\(t\ dump\ /. Times -> List\) /. Power[_, n_] :> {0, n}\) /. dummy -> 0]]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Misc", "Subsection", CellTags->"T1.3.7.1"], Cell[BoxData[ \(PreFactor /: \t\tPreFactor[a_]^n_ := PreFactor[a^n]\)], "Input"], Cell[CellGroupData[{ Cell["Colors", "Subsubsection", CellTags->"T1.3.7.1.1"], Cell[TextData[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], " ", StyleBox["TVI ", FontColor->RGBColor[0.2, 0.4, 0.8]], StyleBox["TFR ", FontColor->RGBColor[0, 0.6, 0]], StyleBox["TVR ", FontColor->RGBColor[0.2, 0.8, 1]], StyleBox["MakeFun ", FontColor->RGBColor[1, 0.6, 0.6]], StyleBox["Cayley ", FontColor->RGBColor[1, 0, 0.4]], StyleBox["CayleyD ", FontColor->RGBColor[1, 0.2, 1]], StyleBox["Cayleyu", FontColor->RGBColor[0.8, 0.8, 0.4]], StyleBox[" ", FontColor->RGBColor[1, 0.2, 1]], StyleBox["IFF ", FontColor->RGBColor[0.6, 0.4, 1]], StyleBox["ToArgs ", FontColor->RGBColor[0.2, 0.6, 1]], StyleBox["Block", FontSize->16, FontWeight->"Bold", FontColor->RGBColor[1, 0.2, 0.2]] }], "Text"], Cell[BoxData[ \(\((MakeBoxes[Block, \ StandardForm]\ := \ \n\ \ \ \ StyleBox["\", \ Rule[FontSize, \ 16], \ \n\ \ \ \ \ Rule[FontWeight, \ "\"], \ \n\ \ \ \ \ Rule[FontColor, \ RGBColor[1, \ 0.2, \ 0.2]]])\); \n\ \ \((MakeBoxes[Cayley, \ StandardForm]\ := \ \n\ \ \ \ StyleBox["\", \ Rule[FontColor, \ RGBColor[1, \ 0, \ 0.4]]]) \); \n\ \ \(( MakeBoxes[CayleyD, \ StandardForm]\ := \ \n\ \ \ \ StyleBox["\", \ Rule[FontColor, \ RGBColor[1, \ 0.2, \ 1]]]) \); \n\ \ \(( MakeBoxes[Cayleyu, \ StandardForm]\ := \ \n\ \ \ \ StyleBox["\", \ Rule[FontColor, \ \n\ \ \ \ \ \ RGBColor[0.8, \ 0.8, \ 0.4]]])\); \n \ \ \((MakeBoxes[IFF, \ StandardForm]\ := \ \n\ \ \ \ StyleBox["\", \ Rule[FontColor, \ RGBColor[0.6, \ 0.4, \ 1]]]) \); \n\ \ \(( MakeBoxes[MakeFun, \ StandardForm]\ := \ \n\ \ \ \ StyleBox["\", \ Rule[FontColor, \ RGBColor[1, \ 0.6, \ 0.6]]]\n)\); \((MakeBoxes[TFI, \ StandardForm]\ := \ \n\ \ \ \ StyleBox["\", \ Rule[FontColor, \ RGBColor[1, \ 0.6, \ 0]]])\); \n\ \ \((MakeBoxes[TFR, \ StandardForm]\ := \ \n\ \ \ \ StyleBox["\", \ Rule[FontColor, \ RGBColor[0, \ 0.6, \ 0]]])\); \n\ \ \((MakeBoxes[ToArgs, \ StandardForm]\ := \ \n\ \ \ \ StyleBox["\", \ Rule[FontColor, \ RGBColor[0.2, \ 0.6, \ 1]]])\); \n\ \ \((MakeBoxes[TVI, \ StandardForm]\ := \ \n\ \ \ \ StyleBox["\", \ Rule[FontColor, \ RGBColor[0.2, \ 0.4, \ 0.8]]]) \); \n\ \ \(( MakeBoxes[TVR, \ StandardForm]\ := \ \n\ \ \ \ StyleBox["\", \ Rule[FontColor, \ RGBColor[0.2, \ 0.8, \ 1]]]) \)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["PQ", "Subsubsection", CellTags->"T1.3.7.2.1"], Cell[BoxData[ \(\(PQ[_Integer?Positive]\ := \ True; \)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["PNQ", "Subsubsection", CellTags->"T1.3.7.3.1"], Cell[BoxData[ \(\(PNQ[0] = True; \)\)], "Input"], Cell[BoxData[ \(\(PNQ[_Integer?Positive]\ := \ True; \)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["FactorC", "Subsubsection", CellTags->"T1.3.7.4.1"], Cell[BoxData[ \(FactorC[z_]\ := \ \(FactorC[z] = Factor[z]\)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["TFI", "Subsubsection", CellTags->"T1.3.7.5.1"], Cell[BoxData[ \(TFI[depp__, {a___, b_Integer, c___}] := \n\tTFI[depp, {a, {b, 0}, c}]; \nTFI[depp__, {a___, {0, m_ /; m =!= 0}, b___}] := \n\t\ TFI[depp, {a, {0, 0}, b}]; \n TFI[a__, {0, 0}, b__List] := \n\tTFI[a, b]; \n TFI[d_, pp_, dp_, {0, 0}, {x1_, x2_, x3_, x4_, x5_}, list_List] := TFI[d, pp, {x1, x2, x3, x4, x5}, list]; \n TFI[d_, pp_, dp_, {a_, b_}, {0, 0, 0, 0, 0}, list_List] := TFI[d, pp, dp, {a, b}, list]; \n TFI[d_, pp_, dp_ /; Head[dp] =!= List, {0, 0, 0, 0, 0}, list_List] := TFI[d, pp, list]; \n TFI[d_, pp_, dp_ /; Head[dp] =!= List, list_List] := TFI[d, pp, list]; \n TFI[d_, pp_, dp_ /; Head[dp] =!= List, {x1_, x2_, x3_, x4_, x5_}, list_List] := TFI[d, pp, {x1, x2, x3, x4, x5}, list]; \)], "Input"], Cell[BoxData[ \(TFI[__, \ {\ {_, _}, {0, 0}, {_, _}, {0, 0}, {_, 0}\ }]\ := \ 0\ ; \n TFI[__, \ {\ {0, 0}, {_, _}, {0, 0}, {_, _}, {_, 0}\ }]\ := \ 0\ ; \n TFI[__, \ {\ {0, 0}, {_, _}, {_, 0}, {_, _}, {0, 0}\ }]\ := \ 0\ ; \n TFI[__, \ {\ {_, 0}, {_, _}, {0, 0}, {_, _}, {0, 0}\ }]\ := \ 0\ ; \n TFI[__, \ {\ {_, _}, {_, 0}, {_, _}, {0, 0}, {0, 0}\ }]\ := \ 0\ ; \n TFI[__, \ {\ {_, _}, {0, 0}, {_, _}, {_, 0}, {0, 0}\ }]\ := \ 0\ ; \n TFI[__, \ {\ {0, 0}, {0, 0}, {0, 0}, {_, 0}, {_, _}\ }]\ := \ 0\ ; \n TFI[__, \ {\ {0, 0}, {0, 0}, {_, 0}, {0, 0}, {_, _}\ }]\ := \ 0\ ; \n TFI[__, \ {\ {0, 0}, {_, 0}, {0, 0}, {0, 0}, {_, _}\ }]\ := \ 0\ ; \n TFI[__, \ {\ {_, 0}, {0, 0}, {0, 0}, {0, 0}, {_, _}\ }]\ := \ 0\ ; \n TFI[__, \ {\ {_, _}, {_, 0}, {0, 0}, {0, 0}, {0, 0}\ }]\ := \ 0\ ; \n TFI[__, \ {\ {_, 0}, {_, _}, {0, 0}, {0, 0}, {0, 0}\ }]\ := \ 0\ ; \n TFI[__, \ {\ {_, _}, {0, 0}, {0, 0}, {_, 0}, {0, 0}\ }]\ := \ 0\ ; \n TFI[__, \ {\ {_, 0}, {0, 0}, {0, 0}, {_, _}, {0, 0}\ }]\ := \ 0\ ; \n TFI[__, \ {\ {0, 0}, {_, 0}, {_, _}, {0, 0}, {0, 0}\ }]\ := \ 0\ ; \n TFI[__, \ {\ {0, 0}, {_, _}, {_, 0}, {0, 0}, {0, 0}\ }]\ := \ 0\ ; \n TFI[__, \ {\ {0, 0}, {0, 0}, {_, _}, {_, 0}, {0, 0}\ }]\ := \ 0\ ; \n TFI[__, \ {\ {0, 0}, {0, 0}, {_, 0}, {_, _}, {0, 0}\ }]\ := \ 0\ ; \)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["TJI", "Subsubsection", CellTags->"T1.3.7.6.1"], Cell["\<\ TJI[de_, pp_, {{n1_Integer, m1_}, {n2_Integer, m2_}, {n3_Integer, m3_}}] := (TJI[de, pp, {{n1, m1}, {n2, m2}, {n3, m3}}] = TJI[de, pp, Reverse[Sort[{{n1, m1}, {n2, m2}, {n3, m3}}]]]) /; !OrderedQ[{{n3, m3}, {n2, m2}, {n1, m1}}] \ \>", "Input"], Cell[BoxData[ \(TJI[d, pp, {{1, m1}, {1, m2}, {1, m3}}]\)], "Input"], Cell[BoxData[ \(TJI[d_, 0, {{_, 0}, {_, 0}, {_, 0}}] := 0\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["TBI", "Subsubsection", CellTags->"T1.3.7.7.1"], Cell[BoxData[ RowBox[{ RowBox[{ StyleBox["TBI", FontColor->RGBColor[1, 0.6, 0]], "[", \(de_, pp_, {{n1_Integer, m1_}, {n2_Integer, m2_}}\), "]"}], ":=", RowBox[{ RowBox[{"(", RowBox[{\(TJI[de, pp, {{n1, m1}, {n2, m2}}]\), "=", RowBox[{ StyleBox["TBI", FontColor->RGBColor[1, 0.6, 0]], "[", \(de, pp, Reverse@\(Sort@{{n1, m1}, {n2, m2}}\)\), "]"}]}], ")"}], "/;", "\[InvisibleSpace]", \(! \((OrderedQ[{{n2, m2}, {n1, m1}}])\)\)}]}]], "Input"], Cell[BoxData[ \(TBI[d_, 0, {{_, 0}, {_, 0}}] := 0\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["TAI", "Subsubsection", CellTags->"T1.3.7.8.1"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ StyleBox["TAI", FontColor->RGBColor[1, 0.6, 0]], "[", \(de_, pp_, {{n1_Integer, 0}}\), "]"}], ":=", "0"}], ";"}]], "Input"] }, Closed]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Definitions and notation", "Section", CellDingbat->"\[FilledSmallCircle]", CellTags->"T1.4.1"], Cell[BoxData[ RowBox[{ RowBox[{"\[CapitalDelta]\[ScriptCapitalC]", "=", RowBox[{\(-\(1\/2\)\), RowBox[{"Det", "[", " ", RowBox[{"(", GridBox[{ {"0", "1", "1", "1", "1"}, {"1", "0", \(\[Mu]\_6\), \(\[Mu]\_4\), \(\[Mu]\_3\)}, {"1", \(\[Mu]\_6\), "0", \(\[Mu]\_2\), \(\[Mu]\_1\)}, {"1", \(\[Mu]\_4\), \(\[Mu]\_2\), "0", \(\[Mu]\_5\)}, {"1", \(\[Mu]\_3\), \(\[Mu]\_1\), \(\[Mu]\_5\), "0"} }], ")"}], "]"}]}]}], ";"}]], "Input"], Cell[BoxData[ \(\(checkli\ = \ {\n\t\t\[ScriptCapitalC] -> \[CapitalDelta]\[ScriptCapitalC], \n \[CapitalDelta]\_i_ :> \[PartialD]\_\(\[Mu]\_i\)\[CapitalDelta]\[ScriptCapitalC], \n\t\t \[Mu]\_6 :> PP, \[Mu]\_i_ :> ToExpression["\"<>ToString[i]]^2, \n \t\tm\_1 :> \@m1\^2, m\_2 :> \@m2\^2, m\_3 :> \@m3\^2, m\_4 :> \@m4\^2, m\_5 :> \@m5\^2, \n \[CapitalDelta]\_\(i_, j_, k_\) :> \[Mu]\_i\%2 + \[Mu]\_j\%2 + \[Mu]\_k\%2 - 2 \((\(\[Mu]\_i\) \[Mu]\_j + \(\[Mu]\_j\) \[Mu]\_k + \(\[Mu]\_k\) \[Mu]\_i)\), \n u\_\(i_, j_, k_\) :> \[Mu]\_i - \[Mu]\_j - \[Mu]\_k, \n \[CapitalSigma]\_i_ :> 3\ d\ - 2\ \((\[Sum]\_\(j = 1\)\%i \[Nu]\_j)\) - 2, \n\t \[Nu]\_1 \[RuleDelayed] n1, \[Nu]\_2 \[RuleDelayed] n2, \[Nu]\_3 \[RuleDelayed] n3, \[Nu]\_4 \[RuleDelayed] n4, \[Nu]\_5 \[RuleDelayed] n5}; \)\)], "Input"], Cell[TextData[{ "Define symmetry property for ", Cell[BoxData[ \(TraditionalForm\`\[CapitalDelta]\_\(i, j, k\)\)]] }], "Text"], Cell[BoxData[ \(\[CapitalDelta]\_\(i_, j_, k_\) := \[CapitalDelta]\_\(Sequence@@Sort[{i, j, k}]\) /; \(! OrderedQ[{i, j, k}]\)\)], "Input"], Cell[BoxData[ \(\[CapitalDelta]\_\(3, 1, 2\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ StyleBox["ToArgs", FontColor->RGBColor[0.2, 0.6, 1]]], "Subsection", CellTags->"T1.4.1.1"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ StyleBox["ToArgs", FontColor->RGBColor[0.2, 0.6, 1]], "[", "z_", "]"}], ":=", \(Expand[z //. checkli]\)}], ";"}]], "Input"], Cell[BoxData[ \(ToArgs[\[CapitalSigma]\_4] // InputForm\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox["Cayley", FontColor->RGBColor[1, 0, 0.4]]], "Subsection", CellTags->"T1.4.2.1"], Cell[TextData[{ "This is (40). ( p = ", Cell[BoxData[ \(TraditionalForm\`\@p\^2\)]], ")" }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{"setd", "[", RowBox[{ RowBox[{"hCayley", "[", RowBox[{ RowBox[{ InterpretationBox[\(m\_1\), m1], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_2\), m2], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_3\), m3], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_4\), m4], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_5\), m5], ":", "_"}], ",", "p_"}], "]"}], ",", RowBox[{"set", "[", RowBox[{ RowBox[{"hCayley", "[", RowBox[{ InterpretationBox[\(m\_1\), m1], ",", InterpretationBox[\(m\_2\), m2], ",", InterpretationBox[\(m\_3\), m3], ",", InterpretationBox[\(m\_4\), m4], ",", InterpretationBox[\(m\_5\), m5], ",", "p"}], "]"}], ",", RowBox[{"factor", "[", RowBox[{ RowBox[{ StyleBox["ToArgs", FontColor->RGBColor[0.2, 0.6, 1]], "[", "\[ScriptCapitalC]", "]"}], "/.", RowBox[{ InterpretationBox[\(p\^2\), PP], "\[Rule]", \(p\^2\)}]}], "]"}]}], "]"}]}], "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"hCayley", "\[RuleDelayed]", StyleBox["Cayley", FontColor->RGBColor[1, 0, 0.4]]}], ",", \(setd \[RuleDelayed] SetDelayed\), ",", \(set \[RuleDelayed] Set\), ",", \(factor \[RuleDelayed] Factor\)}], "}"}]}]], "Input"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ StyleBox["Cayley", FontColor->RGBColor[1, 0, 0.4]], "[", "i", "]"}], "=", \(\[CapitalDelta]\_i\)}]], "Subsection", CellTags->"T1.4.3.1"], Cell[BoxData[ RowBox[{"Do", "[", RowBox[{ RowBox[{ RowBox[{"setd", "[", RowBox[{ RowBox[{\(hCayley[i]\), "[", RowBox[{"{", RowBox[{ RowBox[{ InterpretationBox[\(m\_1\), m1], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_2\), m2], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_3\), m3], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_4\), m4], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_5\), m5], ":", "_"}], ",", "p_"}], "}"}], "]"}], ",", RowBox[{"set", "[", RowBox[{ RowBox[{\(hCayley[i]\), "[", RowBox[{"{", RowBox[{ InterpretationBox[\(m\_1\), m1], ",", InterpretationBox[\(m\_2\), m2], ",", InterpretationBox[\(m\_3\), m3], ",", InterpretationBox[\(m\_4\), m4], ",", InterpretationBox[\(m\_5\), m5], ",", "p"}], "}"}], "]"}], ",", RowBox[{"factor", "[", RowBox[{ RowBox[{ StyleBox["ToArgs", FontColor->RGBColor[0.2, 0.6, 1]], "[", \(\[CapitalDelta]\_i\), "]"}], "/.", RowBox[{ InterpretationBox[\(p\^2\), PP], "\[Rule]", \(p\^2\)}]}], "]"}]}], "]"}]}], "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"hCayley", "\[RuleDelayed]", StyleBox["Cayley", FontColor->RGBColor[1, 0, 0.4]]}], ",", \(setd \[RuleDelayed] SetDelayed\), ",", \(set \[RuleDelayed] Set\), ",", \(factor \[RuleDelayed] Factor\)}], "}"}]}], ",", \({i, 6}\)}], "]"}]], "Input"], Cell[BoxData[ RowBox[{ StyleBox["ToArgs", FontColor->RGBColor[0.2, 0.6, 1]], "[", \(\[CapitalDelta]\_\(1, 2, 6\)\), "]"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{ StyleBox["Cayley", FontColor->RGBColor[1, 0, 0.4]], "[", \(i_, j_, k_\), "]"}], "[", "m_List", "]"}], ":=", RowBox[{ RowBox[{ RowBox[{ StyleBox["Cayley", FontColor->RGBColor[1, 0, 0.4]], "[", \(i, j, k\), "]"}], "[", "m", "]"}], "=", \(Block[{mm = m}, \n\t\t\t While[Length[mm] < 7, AppendTo[mm, Last[mm]]]; \n\t\t\t FactorC[mm\[LeftDoubleBracket]i\[RightDoubleBracket]\^4 - 2\ mm\[LeftDoubleBracket]j\[RightDoubleBracket]\^2\ mm\[LeftDoubleBracket]i\[RightDoubleBracket]\^2 - 2\ mm\[LeftDoubleBracket]k\[RightDoubleBracket]\^2\ mm\[LeftDoubleBracket]i\[RightDoubleBracket]\^2 + mm\[LeftDoubleBracket]j\[RightDoubleBracket]\^4 + mm\[LeftDoubleBracket]k\[RightDoubleBracket]\^4 - 2\ mm\[LeftDoubleBracket]j\[RightDoubleBracket]\^2\ mm\[LeftDoubleBracket]k\[RightDoubleBracket]\^2]]\)}]}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{ StyleBox["Cayleyu", FontColor->RGBColor[0.8, 0.8, 0.4]], "[", \(i_, j_, k_\), "]"}], "[", "m_List", "]"}], ":=", RowBox[{ RowBox[{ RowBox[{ StyleBox["Cayleyu", FontColor->RGBColor[0.8, 0.8, 0.4]], "[", \(i, j, k\), "]"}], "[", "mm", "]"}], "=", \(Block[{mm = m}, \n\t\t\t\t\t While[Length[mm] < 7, AppendTo[mm, Last[mm]]]; FactorC[mm\[LeftDoubleBracket]i\[RightDoubleBracket]\^2 - mm\[LeftDoubleBracket]j\[RightDoubleBracket]\^2 - mm\[LeftDoubleBracket]k\[RightDoubleBracket]\^2]]\)}]}], ";"}]], "Input"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ StyleBox["CayleyD", FontColor->RGBColor[1, 0.2, 1]], "[", "i", "]"}], "=", \(\[CapitalDelta]\_i\/\[CapitalDelta]\)}]], "Subsection", CellTags->"T1.4.4.1"], Cell[BoxData[ RowBox[{"Do", "[", RowBox[{ RowBox[{ RowBox[{"setd", "[", RowBox[{ RowBox[{\(hCayleyD[i]\), "[", RowBox[{"{", RowBox[{ RowBox[{ InterpretationBox[\(m\_1\), m1], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_2\), m2], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_3\), m3], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_4\), m4], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_5\), m5], ":", "_"}], ",", "p_"}], "}"}], "]"}], ",", RowBox[{"set", "[", RowBox[{ RowBox[{\(hCayleyD[i]\), "[", RowBox[{"{", RowBox[{ InterpretationBox[\(m\_1\), m1], ",", InterpretationBox[\(m\_2\), m2], ",", InterpretationBox[\(m\_3\), m3], ",", InterpretationBox[\(m\_4\), m4], ",", InterpretationBox[\(m\_5\), m5], ",", "p"}], "}"}], "]"}], ",", RowBox[{"factor", "[", FractionBox[ RowBox[{ RowBox[{ StyleBox["ToArgs", FontColor->RGBColor[0.2, 0.6, 1]], "[", \(\[CapitalDelta]\_i\), "]"}], "/.", RowBox[{ InterpretationBox[\(p\^2\), PP], "\[Rule]", \(p\^2\)}]}], RowBox[{"\[ScriptCapitalC]", "[", RowBox[{ InterpretationBox[\(m\_1\), m1], ",", InterpretationBox[\(m\_2\), m2], ",", InterpretationBox[\(m\_3\), m3], ",", InterpretationBox[\(m\_4\), m4], ",", InterpretationBox[\(m\_5\), m5], ",", "p"}], "]"}]], "]"}]}], "]"}]}], "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"hCayleyD", "\[RuleDelayed]", StyleBox["CayleyD", FontColor->RGBColor[1, 0.2, 1]]}], ",", \(setd \[RuleDelayed] SetDelayed\), ",", \(set \[RuleDelayed] Set\), ",", \(factor \[RuleDelayed] Factor\), ",", RowBox[{"\[ScriptCapitalC]", "\[RuleDelayed]", StyleBox["Cayley", FontColor->RGBColor[1, 0, 0.4]]}]}], "}"}]}], ",", \({i, 6}\)}], "]"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"setd", "[", RowBox[{ RowBox[{\(hCayleyD[1, 2, 5]\), "[", RowBox[{"{", RowBox[{ RowBox[{ InterpretationBox[\(m\_1\), m1], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_2\), m2], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_3\), m3], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_4\), m4], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_5\), m5], ":", "_"}], ",", "p_"}], "}"}], "]"}], ",", RowBox[{"set", "[", RowBox[{ RowBox[{\(hCayleyD[1, 2, 5]\), "[", RowBox[{"{", RowBox[{ InterpretationBox[\(m\_1\), m1], ",", InterpretationBox[\(m\_2\), m2], ",", InterpretationBox[\(m\_3\), m3], ",", InterpretationBox[\(m\_4\), m4], ",", InterpretationBox[\(m\_5\), m5], ",", "p"}], "}"}], "]"}], ",", RowBox[{"factor", "[", FractionBox[ RowBox[{ RowBox[{ StyleBox["ToArgs", FontColor->RGBColor[0.2, 0.6, 1]], "[", \(\[CapitalDelta]\_\(1, 2, 5\)\), "]"}], "/.", RowBox[{ InterpretationBox[\(p\^2\), PP], "\[Rule]", \(p\^2\)}]}], RowBox[{"\[ScriptCapitalC]", "[", RowBox[{ InterpretationBox[\(m\_1\), m1], ",", InterpretationBox[\(m\_2\), m2], ",", InterpretationBox[\(m\_3\), m3], ",", InterpretationBox[\(m\_4\), m4], ",", InterpretationBox[\(m\_5\), m5], ",", "p"}], "]"}]], "]"}]}], "]"}]}], "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"hCayleyD", "\[RuleDelayed]", StyleBox["CayleyD", FontColor->RGBColor[1, 0.2, 1]]}], ",", \(setd \[RuleDelayed] SetDelayed\), ",", \(set \[RuleDelayed] Set\), ",", \(factor \[RuleDelayed] Factor\), ",", RowBox[{"\[ScriptCapitalC]", "\[RuleDelayed]", StyleBox["Cayley", FontColor->RGBColor[1, 0, 0.4]]}]}], "}"}]}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"setd", "[", RowBox[{ RowBox[{\(hCayleyD[1, 3, 6]\), "[", RowBox[{"{", RowBox[{ RowBox[{ InterpretationBox[\(m\_1\), m1], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_2\), m2], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_3\), m3], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_4\), m4], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_5\), m5], ":", "_"}], ",", "p_"}], "}"}], "]"}], ",", RowBox[{"set", "[", RowBox[{ RowBox[{\(hCayleyD[1, 3, 6]\), "[", RowBox[{"{", RowBox[{ InterpretationBox[\(m\_1\), m1], ",", InterpretationBox[\(m\_2\), m2], ",", InterpretationBox[\(m\_3\), m3], ",", InterpretationBox[\(m\_4\), m4], ",", InterpretationBox[\(m\_5\), m5], ",", "p"}], "}"}], "]"}], ",", RowBox[{"factor", "[", FractionBox[ RowBox[{ RowBox[{ StyleBox["ToArgs", FontColor->RGBColor[0.2, 0.6, 1]], "[", \(\[CapitalDelta]\_\(1, 3, 6\)\), "]"}], "/.", RowBox[{ InterpretationBox[\(p\^2\), PP], "\[Rule]", \(p\^2\)}]}], RowBox[{"\[ScriptCapitalC]", "[", RowBox[{ InterpretationBox[\(m\_1\), m1], ",", InterpretationBox[\(m\_2\), m2], ",", InterpretationBox[\(m\_3\), m3], ",", InterpretationBox[\(m\_4\), m4], ",", InterpretationBox[\(m\_5\), m5], ",", "p"}], "]"}]], "]"}]}], "]"}]}], "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"hCayleyD", "\[RuleDelayed]", StyleBox["CayleyD", FontColor->RGBColor[1, 0.2, 1]]}], ",", \(setd \[RuleDelayed] SetDelayed\), ",", \(set \[RuleDelayed] Set\), ",", \(factor \[RuleDelayed] Factor\), ",", RowBox[{"\[ScriptCapitalC]", "\[RuleDelayed]", StyleBox["Cayley", FontColor->RGBColor[1, 0, 0.4]]}]}], "}"}]}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"setd", "[", RowBox[{ RowBox[{\(hCayleyD[3, 4, 5]\), "[", RowBox[{"{", RowBox[{ RowBox[{ InterpretationBox[\(m\_1\), m1], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_2\), m2], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_3\), m3], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_4\), m4], ":", "_"}], ",", RowBox[{ InterpretationBox[\(m\_5\), m5], ":", "_"}], ",", "p_"}], "}"}], "]"}], ",", RowBox[{"set", "[", RowBox[{ RowBox[{\(hCayleyD[3, 4, 5]\), "[", RowBox[{"{", RowBox[{ InterpretationBox[\(m\_1\), m1], ",", InterpretationBox[\(m\_2\), m2], ",", InterpretationBox[\(m\_3\), m3], ",", InterpretationBox[\(m\_4\), m4], ",", InterpretationBox[\(m\_5\), m5], ",", "p"}], "}"}], "]"}], ",", RowBox[{"factor", "[", FractionBox[ RowBox[{ RowBox[{ StyleBox["ToArgs", FontColor->RGBColor[0.2, 0.6, 1]], "[", \(\[CapitalDelta]\_\(3, 4, 5\)\), "]"}], "/.", RowBox[{ InterpretationBox[\(p\^2\), PP], "\[Rule]", \(p\^2\)}]}], RowBox[{"\[ScriptCapitalC]", "[", RowBox[{ InterpretationBox[\(m\_1\), m1], ",", InterpretationBox[\(m\_2\), m2], ",", InterpretationBox[\(m\_3\), m3], ",", InterpretationBox[\(m\_4\), m4], ",", InterpretationBox[\(m\_5\), m5], ",", "p"}], "]"}]], "]"}]}], "]"}]}], "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"hCayleyD", "\[RuleDelayed]", StyleBox["CayleyD", FontColor->RGBColor[1, 0.2, 1]]}], ",", \(setd \[RuleDelayed] SetDelayed\), ",", \(set \[RuleDelayed] Set\), ",", \(factor \[RuleDelayed] Factor\), ",", RowBox[{"\[ScriptCapitalC]", "\[RuleDelayed]", StyleBox["Cayley", FontColor->RGBColor[1, 0, 0.4]]}]}], "}"}]}]], "Input"], Cell[BoxData[ RowBox[{ StyleBox["ToArgs", FontColor->RGBColor[0.2, 0.6, 1]], "[", \(\[CapitalDelta]\_\(i, j, k\)\), "]"}]], "Input"], Cell[BoxData[ RowBox[{ StyleBox["ToArgs", FontColor->RGBColor[0.2, 0.6, 1]], "[", \(\[CapitalDelta]\_\(1, 2, 6\)\), "]"}]], "Input"], Cell[BoxData[ RowBox[{ StyleBox["ToArgs", FontColor->RGBColor[0.2, 0.6, 1]], "[", \(u\_\(i, j, k\)\), "]"}]], "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Utility Functions", "Section", CellDingbat->"\[FilledSmallCircle]", CellTags->"T1.5.1"], Cell[CellGroupData[{ Cell["MakeFun and friends", "Subsection", CellTags->"T1.5.1.1"], Cell["\<\ This function generates the recursion function definitions for TARCER starting from the entered relations.\ \>", "Text"], Cell["The idea is to recurse TFR into TFI's step by step.", "Text"], Cell[TextData[{ "Define: S cD[ijk__] := ", Cell[BoxData[ \(TraditionalForm \`\(\[ScriptCapitalC]\^\(-1\)\) \[CapitalDelta]\_ijk\)]] }], "Text"], Cell[BoxData[ \(\(nutonand\[CapitalDelta]u[w_, 5] := \(w /. {\[Nu]\_1 \[RuleDelayed] n1, \[Nu]\_2 \[RuleDelayed] n2, \[Nu]\_3 \[RuleDelayed] n3, \[Nu]\_4 \[RuleDelayed] n4, \[Nu]\_5 \[RuleDelayed] n5, \[CapitalDelta]\_ijk__ \[RuleDelayed] \[ScriptCapitalC]\ cD[ijk], u\_ijk__ \[RuleDelayed] cu[ijk], \n\t\tD\_ijk__ :> TA[D, ijk], \[Rho]\_ijk__ :> TA[\[Rho], ijk], \[Phi]\_\(ijk__\ \) :> TA[\[Phi], ijk], \n\t\t\t \[Sigma]\_\(i_, j_, k_\) :> TA[\[Sigma], d, i, j, k, \[Nu]\_i, \[Nu]\_j, \[Nu]\_k], h\_\(i_, j_, k_\) :> TA[h, d, i, j, k, \[Nu]\_i, \[Nu]\_j, \[Nu]\_k], S\_\(i_, j_, k_\) :> TA[S, d, i, j, k, \[Nu]\_i, \[Nu]\_j, \[Nu]\_k], \n\t\t\t \[CapitalSigma]\_i_ :> ToArgs[\[CapitalSigma]\_i]\n\t\t}\) /. {\t \[Nu]\_1 \[RuleDelayed] n1, \[Nu]\_2 \[RuleDelayed] n2, \[Nu]\_3 \[RuleDelayed] n3, \[Nu]\_4 \[RuleDelayed] n4, \[Nu]\_5 \[RuleDelayed] n5, m\_1 :> m1, m\_2 :> m2, m\_3 :> m3, m\_4 :> m4, m\_5 :> m5}; \)\)], "Input"], Cell[BoxData[ \(\(nutonand\[CapitalDelta]u[w_] := \(w /. {\[Nu]\_1 \[RuleDelayed] n1, \[Nu]\_2 \[RuleDelayed] n2, \[Nu]\_3 \[RuleDelayed] n3, \[Nu]\_4 \[RuleDelayed] n4, \[Nu]\_5 \[RuleDelayed] n5, \[CapitalDelta]\_ijk__ \[RuleDelayed] cD[ijk], u\_ijk__ \[RuleDelayed] cu[ijk], \n\t\tD\_ijk__ :> TA[D, ijk], \[Rho]\_ijk__ :> TA[\[Rho], ijk], \[Phi]\_\(ijk__\ \) :> TA[\[Phi], ijk], \n\t\t\t \[Sigma]\_\(i_, j_, k_\) :> TA[\[Sigma], d, i, j, k, \[Nu]\_i, \[Nu]\_j, \[Nu]\_k], h\_\(i_, j_, k_\) :> TA[h, d, i, j, k, \[Nu]\_i, \[Nu]\_j, \[Nu]\_k], S\_\(i_, j_, k_\) :> TA[S, d, i, j, k, \[Nu]\_i, \[Nu]\_j, \[Nu]\_k], \n\t\t\t \[CapitalSigma]\_i_ :> ToArgs[\[CapitalSigma]\_i]\n\t\t}\) /. {\t \[Nu]\_1 \[RuleDelayed] n1, \[Nu]\_2 \[RuleDelayed] n2, \[Nu]\_3 \[RuleDelayed] n3, \[Nu]\_4 \[RuleDelayed] n4, \[Nu]\_5 \[RuleDelayed] n5, m\_1 :> m1, m\_2 :> m2, m\_3 :> m3, m\_4 :> m4, m\_5 :> m5}; \)\)], "Input"], Cell[BoxData[ \(\(addPeP[TFR[d_, pp_, li1_, rest_]] := TFR[d, pp, li1, rest]; \)\)], "Input"], Cell[BoxData[ \(\(addPeP[TFI[d_, pp_, li1_List]] := TFI[d, pp, li1]; \)\)], "Input"], Cell[BoxData[ \(\(addPeP[TFR[d_, pp_, dp_Symbol, li1_, rest_]] := TFR[d, pp, dp, li1, rest]; \)\)], "Input"], Cell[BoxData[ \(\(addPeP[TFI[d_, pp_, dp_Symbol, li1_List]] := TFI[d, pp, dp, li1]; \)\)], "Input"], Cell[BoxData[ \(\(addPeP[TVI[d_, pp_, li1_List]] := TVI[d, pp, li1]; \)\)], "Input"], Cell[BoxData[ \(nnnnnaddPeP[any_[d_, pp_, li1_List, rest__List]] := any[d, pp, li1, rest] /; any =!= List\)], "Input"], Cell[BoxData[{ RowBox[{ RowBox[{\(addPeP[z_List]\), ":=", RowBox[{"Append", "[", RowBox[{"z", ",", SqrtBox[ InterpretationBox[\(p\^2\), PP]]}], "]"}]}], ";", RowBox[{ RowBox[{"addPeP", "[", RowBox[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], "[", \(d_, z_List\), "]"}], "]"}], ":=", RowBox[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], "[", RowBox[{"d", ",", InterpretationBox[\(p\^2\), PP], ",", "z"}], "]"}]}], ";"}], RowBox[{ RowBox[{ RowBox[{"addPeP", "[", RowBox[{ StyleBox["TVI", FontColor->RGBColor[0.2, 0.4, 0.8]], "[", \(d_, z_List\), "]"}], "]"}], ":=", RowBox[{ StyleBox["TVI", FontColor->RGBColor[0.2, 0.4, 0.8]], "[", RowBox[{"d", ",", InterpretationBox[\(p\^2\), PP], ",", "z"}], "]"}]}], ";", RowBox[{\(addPeP[TJI[d_, z_List]]\), ":=", RowBox[{"TJI", "[", RowBox[{"d", ",", InterpretationBox[\(p\^2\), PP], ",", "z"}], "]"}]}], ";"}], RowBox[{ RowBox[{ RowBox[{"addPeP", "[", RowBox[{ StyleBox["TFR", FontColor->RGBColor[0, 0.6, 0]], "[", \(d_, z_List\), "]"}], "]"}], ":=", RowBox[{ StyleBox["TFR", FontColor->RGBColor[0, 0.6, 0]], "[", RowBox[{"d", ",", RowBox[{ InterpretationBox[\(p\^2\), PP], ":", "_"}], ",", "z"}], "]"}]}], ";"}], RowBox[{ RowBox[{ RowBox[{"addPeP", "[", RowBox[{ StyleBox["TFR", FontColor->RGBColor[0, 0.6, 0]], "[", \(d_, pl_List, z_List\), "]"}], "]"}], ":=", RowBox[{ StyleBox["TFR", FontColor->RGBColor[0, 0.6, 0]], "[", RowBox[{"d", ",", RowBox[{ InterpretationBox[\(p\^2\), PP], ":", "_"}], ",", "pl", ",", "z"}], "]"}]}], ";"}], RowBox[{ RowBox[{ RowBox[{"addPeP", "[", RowBox[{ StyleBox["TVR", FontColor->RGBColor[0.2, 0.8, 1]], "[", \(d_, z__List\), "]"}], "]"}], ":=", RowBox[{ StyleBox["TVR", FontColor->RGBColor[0.2, 0.8, 1]], "[", RowBox[{"d", ",", RowBox[{ InterpretationBox[\(p\^2\), PP], ":", "_"}], ",", "z"}], "]"}]}], ";", RowBox[{\(addPeP[TJR[d_, z__List]]\), ":=", RowBox[{"TJR", "[", RowBox[{"d", ",", RowBox[{ InterpretationBox[\(p\^2\), PP], ":", "_"}], ",", "z"}], "]"}]}], ";"}]}], "Input"], Cell[BoxData[ RowBox[{ RowBox[{\(nutomass[w_]\), ":=", RowBox[{ RowBox[{ RowBox[{"w", "/.", RowBox[{"{", RowBox[{ RowBox[{\(\[Nu]\_1 + i1_. \), "\[RuleDelayed]", RowBox[{"{", RowBox[{\(n1 + i1\), ",", InterpretationBox[\(m\_1\), m1]}], "}"}]}], ",", RowBox[{\(\[Nu]\_2 + i2_. \), "\[RuleDelayed]", RowBox[{"{", RowBox[{\(n2 + i2\), ",", InterpretationBox[\(m\_2\), m2]}], "}"}]}], ",", RowBox[{\(\[Nu]\_3 + i3_. \), "\[RuleDelayed]", RowBox[{"{", RowBox[{\(n3 + i3\), ",", InterpretationBox[\(m\_3\), m3]}], "}"}]}], ",", RowBox[{\(\[Nu]\_4 + i4_. \), "\[RuleDelayed]", RowBox[{"{", RowBox[{\(n4 + i4\), ",", InterpretationBox[\(m\_4\), m4]}], "}"}]}], ",", RowBox[{\(\[Nu]\_5 + i5_. \), "\[RuleDelayed]", RowBox[{"{", RowBox[{\(n5 + i5\), ",", InterpretationBox[\(m\_5\), m5]}], "}"}]}]}], "}"}]}], "/.", "\n", \({in1_Integer, in2_Integer, in3_Integer, in4_Integer} :> \n{{in1, m1}, {in2, m2}, {in3, m3}, {in4, m4}}\)}], "/.", \({in1_Integer, in2_Integer, in3_Integer} :> \n{{in1, m1}, {in2, m2}, {in3, m3}}\)}]}], "\n", ";"}]], "Input"], Cell[BoxData[ RowBox[{\(Clear[maybeF]\), ";", RowBox[{\(maybeF[z_Times]\), ":=", RowBox[{\(FactorC[z]\), "/;", RowBox[{ RowBox[{"FreeQ", "[", RowBox[{"z", ",", StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]]}], "]"}], "&&", \(FreeQ[z, TVI]\), "&&", \(FreeQ[z, TJI]\), "&&", \(Length[CC = Cases[z, cD[__], \(-1\)]] > 1\)}]}]}], ";", \(maybeF[z_] := z\), ";", \(SetAttributes[top, Listable]\), ";"}]], "Input"], Cell["This is the function for the information of side conditions.", "Text"], Cell[BoxData[ RowBox[{ RowBox[{"SetAttributes", "[", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], ",", "HoldAll"}], "]"}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{"Clear", "[", StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "]"}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{ RowBox[{ RowBox[{"c_.", " ", RowBox[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], "[", "t__", "]"}]}], "==", "rhs_"}], ",", "eqn_String", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", "conds_", "]"}], ",", \(mrel_ : {}\)}], "]"}], ":=", RowBox[{ StyleBox["Block", CellFrame->True, FontSize->16, FontWeight->"Bold", FontColor->RGBColor[1, 0.2, 0.2]], "[", RowBox[{\({nm}\), ",", RowBox[{ \(nmrel = Select[Flatten[{mrel}], FreeQ[#1, Factor]&]\), ";", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"HoldForm", "@@", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"setdel", "[", RowBox[{ RowBox[{ RowBox[{"addPeP", "[", RowBox[{ StyleBox["TFR", FontColor->RGBColor[0, 0.6, 0]], "@@", \(top/@nutomass[{t}]\)}], "]"}], "/.", "nmrel"}], ",", RowBox[{\(Hold[Condition]\), "[", RowBox[{ RowBox[{ \(Hold[CompoundExpression]\), "[", "\t", RowBox[{ \(\(Hold[TComment]\)[eqn, \(\(\(addPeP[nutomass[TFR[t]]] /. TFR -> TFIC\) /. {Pattern :> pat, Blank :> blank}\) /. pat[PP, blank[]] :> PP\) /. nmrel]\), ",", RowBox[{ RowBox[{"Collect", "[", RowBox[{ RowBox[{"TT", "=", RowBox[{"Expand", "[", RowBox[{ "nutonand\[CapitalDelta]u", "[", RowBox[{ RowBox[{\(1\/c\), RowBox[{"(", RowBox[{"rhs", "/.", RowBox[{ RowBox[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], "[", "te__", "]"}], "\[RuleDelayed]", RowBox[{"addPeP", "[", RowBox[{"nutomass", "[", RowBox[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], "[", "te", "]"}], "]"}], "]"}]}]}], ")"}]}], ",", "5"}], "]"}], "]"}]}], ",", RowBox[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], "[", "__", "]"}], ",", \(maybeF[\((Collect[Numerator[#1], cD[__], Factor]/Collect[Denominator[#1], cD[__], Factor]&)\)/@Factor[#1]]& \)}], "]"}], "/.", "nmrel"}]}], "]"}], ",", RowBox[{ "nutonand\[CapitalDelta]u", "[", RowBox[{ RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", "conds", "]"}], ",", "5"}], "]"}]}], "]"}]}], "]"}], "/.", \(top[i_Integer] \[Rule] i\)}], "/.", \(top \[RuleDelayed] \((patternTest[pattern[#1, blank[]], PQ]&)\)\)}], "/.", RowBox[{ RowBox[{"patternTest", "[", RowBox[{ RowBox[{"pattern", "[", RowBox[{ RowBox[{"dm_", "/;", RowBox[{"MemberQ", "[", RowBox[{ RowBox[{"{", RowBox[{"d", ",", InterpretationBox[\(p\^2\), PP], ",", "DP", ",", InterpretationBox[\(m\_1\), m1], ",", InterpretationBox[\(m\_2\), m2], ",", InterpretationBox[\(m\_3\), m3], ",", InterpretationBox[\(m\_4\), m4], ",", InterpretationBox[\(m\_5\), m5]}], "}"}], ",", "dm"}], "]"}]}], ",", \(blank[]\)}], "]"}], ",", "_"}], "]"}], "\[RuleDelayed]", \(pattern[dm, blank[]]\)}]}], "/.", "\n", "\t\t\t\t\t", \({blank \[RuleDelayed] Blank, pattern \[RuleDelayed] Pattern, patternTest \[RuleDelayed] PatternTest}\)}], "}"}]}], "/.", RowBox[{\(cD[ijk__]\), "\[Rule]", RowBox[{ RowBox[{"Hold", "[", RowBox[{ StyleBox["CayleyD", FontColor->RGBColor[1, 0.2, 1]], "[", "ijk", "]"}], "]"}], "[", \(addPeP[ BLA = \(nutomass[Last[{t}]] /. nmrel \) /. {nuu_, ma_} \[RuleDelayed] ma] \), "]"}]}]}], "/.", \(addPeP -> Identity\)}], "/.", \(Hold[CompoundExpression] \[Rule] CompoundExpression\)}], "/.", RowBox[{ RowBox[{\(Hold[Condition]\), "[", RowBox[{"a_", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", "b_", "]"}]}], "]"}], "\[Rule]", \(a /; b\)}]}], "/.", \(Hold[Set] \[Rule] Set\)}], "/.", \(Hold[TComment] -> TComment\)}], "/.", RowBox[{ RowBox[{"Hold", "[", RowBox[{ StyleBox["CayleyD", FontColor->RGBColor[1, 0.2, 1]], "[", "ijk__", "]"}], "]"}], "\[Rule]", RowBox[{ StyleBox["CayleyD", FontColor->RGBColor[1, 0.2, 1]], "[", "ijk", "]"}]}]}], "/.", \({setdel \[RuleDelayed] SetDelayed}\)}], ")"}], "/.", \(Identity -> identit\)}], "/.", \(identit[a_] -> a\)}]}]}], "]"}]}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{ RowBox[{ RowBox[{"c_.", " ", RowBox[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], "[", "t__", "]"}]}], "==", "rhs_"}], ",", "eqn_String", ",", \(mrel_ : {}\)}], "]"}], ":=", RowBox[{ RowBox[{ StyleBox["Block", CellFrame->True, FontSize->16, FontWeight->"Bold", FontColor->RGBColor[1, 0.2, 0.2]], "[", RowBox[{\({nm}\), ",", RowBox[{ \(nmrel = Select[Flatten[{mrel}], FreeQ[#1, Factor]&]\), ";", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"HoldForm", "@@", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"setdel", "[", RowBox[{ RowBox[{ RowBox[{"addPeP", "[", RowBox[{ StyleBox["TFR", FontColor->RGBColor[0, 0.6, 0]], "@@", \(top/@nutomass[{t}]\)}], "]"}], "/.", "nmrel"}], ",", RowBox[{ \(Hold[CompoundExpression]\), "[", RowBox[{ \(\(Hold[TComment]\)[eqn, \(\(\(addPeP[nutomass[TFR[t]]] /. TFR -> TFIC\) /. {Pattern :> pat, Blank :> blank}\) /. pat[PP, blank[]] :> PP\) /. nmrel]\), ",", RowBox[{ RowBox[{"Collect", "[", RowBox[{ RowBox[{"TT", "=", RowBox[{"Expand", "[", RowBox[{ "nutonand\[CapitalDelta]u", "[", RowBox[{\(1\/c\), RowBox[{"(", RowBox[{"rhs", "/.", RowBox[{ RowBox[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], "[", "te__", "]"}], "\[RuleDelayed]", RowBox[{"addPeP", "[", RowBox[{"nutomass", "[", RowBox[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], "[", "te", "]"}], "]"}], "]"}]}]}], ")"}]}], "]"}], "]"}]}], ",", RowBox[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], "[", "__", "]"}], ",", \(maybeF[\((Collect[Numerator[#1], cD[__], Factor]/Collect[Denominator[#1], cD[__], Factor]&)\)/@Factor[#1]]& \)}], "]"}], "/.", "nmrel"}]}], "]"}]}], "]"}], "/.", \(top[i_Integer] \[Rule] i\)}], "/.", \(top \[RuleDelayed] \((patternTest[pattern[#1, blank[]], PQ]&)\)\)}], "/.", RowBox[{ RowBox[{"patternTest", "[", RowBox[{ RowBox[{"pattern", "[", RowBox[{ RowBox[{"dm_", "/;", RowBox[{"MemberQ", "[", RowBox[{ RowBox[{"{", RowBox[{"d", ",", InterpretationBox[\(p\^2\), PP], ",", "DP", ",", InterpretationBox[\(m\_1\), m1], ",", InterpretationBox[\(m\_2\), m2], ",", InterpretationBox[\(m\_3\), m3], ",", InterpretationBox[\(m\_4\), m4], ",", InterpretationBox[\(m\_5\), m5]}], "}"}], ",", "dm"}], "]"}]}], ",", \(blank[]\)}], "]"}], ",", "_"}], "]"}], "\[RuleDelayed]", \(pattern[dm, blank[]]\)}]}], "/.", "\t", \({blank \[RuleDelayed] Blank, pattern \[RuleDelayed] Pattern, patternTest \[RuleDelayed] PatternTest}\)}], "}"}]}], "/.", RowBox[{\(cD[ijk__]\), "\[Rule]", RowBox[{ RowBox[{"Hold", "[", RowBox[{ StyleBox["CayleyD", FontColor->RGBColor[1, 0.2, 1]], "[", "ijk", "]"}], "]"}], "[", \(addPeP[ \(\(nutomass[Last[{t}]] /. addPeP -> Identity\) /. nmrel \) /. {nuu_, ma_} \[RuleDelayed] ma] \), "]"}]}]}], "/.", \(Hold[CompoundExpression] \[Rule] CompoundExpression\)}], "/.", RowBox[{ RowBox[{\(Hold[Condition]\), "[", RowBox[{"a_", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", "b_", "]"}]}], "]"}], "\[Rule]", \(a /; b\)}]}], "/.", \(Hold[Set] \[Rule] Set\)}], "/.", \(Hold[TComment] -> TComment\)}], "/.", RowBox[{ RowBox[{"Hold", "[", RowBox[{ StyleBox["CayleyD", FontColor->RGBColor[1, 0.2, 1]], "[", "ijk__", "]"}], "]"}], "\[Rule]", RowBox[{ StyleBox["CayleyD", FontColor->RGBColor[1, 0.2, 1]], "[", "ijk", "]"}]}]}], "/.", \({setdel \[RuleDelayed] SetDelayed}\)}], ")"}], "/.", \(addPeP -> Identity\)}], "/.", \(Identity -> identit\)}], "/.", \(identit[a_] -> a\)}]}]}], "]"}], "/;", RowBox[{\(Head[mrel]\), "=!=", StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]]}]}]}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{ RowBox[{ RowBox[{"c_.", " ", RowBox[{ StyleBox["TVI", FontColor->RGBColor[0.2, 0.4, 0.8]], "[", "t__", "]"}]}], "==", "rhs_"}], ",", "eqn_String", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", "conds_", "]"}], ",", \(mrel_ : {}\)}], "]"}], ":=", RowBox[{ StyleBox["Block", FontSize->16, FontWeight->"Bold", FontColor->RGBColor[1, 0.2, 0.2]], "[", RowBox[{\({nm}\), ",", RowBox[{ \(nmrel = Select[Flatten[{mrel}], FreeQ[#1, Factor]&]\), ";", RowBox[{"nmrel", "=", RowBox[{"Join", "[", RowBox[{"nmrel", ",", RowBox[{"{", RowBox[{ RowBox[{\(m\_1\), "\[RuleDelayed]", InterpretationBox[\(m\_1\), m1]}], ",", RowBox[{\(m\_2\), "\[RuleDelayed]", InterpretationBox[\(m\_2\), m2]}], ",", RowBox[{\(m\_3\), "\[RuleDelayed]", InterpretationBox[\(m\_3\), m3]}], ",", RowBox[{\(m\_4\), "\[RuleDelayed]", InterpretationBox[\(m\_4\), m4]}], ",", \(\[CapitalSigma]\_i_ :> ToArgs[\[CapitalSigma]\_i]\)}], "}"}]}], "]"}]}], ";", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"HoldForm", "@@", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"setdel", "[", RowBox[{ RowBox[{ RowBox[{"addPeP", "[", RowBox[{ StyleBox["TVR", FontColor->RGBColor[0.2, 0.8, 1]], "@@", \(top/@nutomass[{t}]\)}], "]"}], "/.", "nmrel"}], ",", RowBox[{\(Hold[Condition]\), "[", RowBox[{ RowBox[{ \(Hold[CompoundExpression]\), "[", RowBox[{ \(\(Hold[TComment]\)[eqn, \(\(\(addPeP[nutomass[TVR[t]]] /. TVR -> TVIC\) /. {Pattern :> pat, Blank :> blank}\) /. pat[PP, blank[]] :> PP\) /. nmrel]\), ",", RowBox[{ RowBox[{ RowBox[{"Collect", "[", RowBox[{ RowBox[{"TT", "=", RowBox[{"Expand", "[", RowBox[{"nutonand\[CapitalDelta]u", "[", RowBox[{\(1\/c\), RowBox[{"(", RowBox[{"rhs", "/.", RowBox[{ RowBox[{ StyleBox["TVI", FontColor->RGBColor[0.2, 0.4, 0.8]], "[", "te__", "]"}], "\[RuleDelayed]", RowBox[{"addPeP", "[", RowBox[{"nutomass", "[", RowBox[{ StyleBox["TVI", FontColor->RGBColor[0.2, 0.4, 0.8]], "[", "te", "]"}], "]"}], "]"}]}]}], ")"}]}], "]"}], "]"}]}], ",", RowBox[{ StyleBox["TVI", FontColor->RGBColor[0.2, 0.4, 0.8]], "[", "__", "]"}], ",", \(maybeF[\((Collect[Numerator[#1], cu[__], Factor]/Collect[Denominator[#1], cu[__], Factor]&)\)/@Factor[#1]]&\)}], "]"}], "/.", \(\[ScriptCapitalC] -> 1\)}], "/.", "nmrel"}]}], "]"}], ",", RowBox[{ "nutonand\[CapitalDelta]u", "[", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", "conds", "]"}], "]"}]}], "]"}]}], "]"}], "/.", \(top[i_Integer] \[Rule] i\)}], "/.", \(top \[RuleDelayed] \((patternTest[pattern[#1, blank[]], PQ]&)\)\)}], "/.", RowBox[{ RowBox[{"patternTest", "[", RowBox[{ RowBox[{"pattern", "[", RowBox[{ RowBox[{"dm_", "/;", RowBox[{"MemberQ", "[", RowBox[{ RowBox[{"{", RowBox[{"d", ",", InterpretationBox[\(p\^2\), PP], ",", InterpretationBox[\(m\_1\), m1], ",", InterpretationBox[\(m\_2\), m2], ",", InterpretationBox[\(m\_3\), m3], ",", InterpretationBox[\(m\_4\), m4]}], "}"}], ",", "dm"}], "]"}]}], ",", \(blank[]\)}], "]"}], ",", "_"}], "]"}], "\[RuleDelayed]", \(pattern[dm, blank[]]\)}]}], "/.", "\t", \({blank \[RuleDelayed] Blank, pattern \[RuleDelayed] Pattern, patternTest \[RuleDelayed] PatternTest}\)}], "}"}]}], "/.", "\n", "\t\t\t", \(HoldPattern[TA[aijk__]] \[Rule] \(Hold[TA[aijk]]\)[ addPeP[\(nutomass[Last[{t}]] /. nmrel \) /. {nuu_, ma_} \[RuleDelayed] ma]] \)}], "/.", "\n", "\t\t\t", \(cD[ijk__] \[Rule] \(Hold[Cayley[ijk]]\)[ addPeP[ \(nutomass[Last[{t}]] /. nmrel \) /. {nuu_, ma_} \[RuleDelayed] ma]] \)}], "/.", RowBox[{\(cu[ijk__]\), "\[Rule]", RowBox[{ RowBox[{"Hold", "[", RowBox[{ StyleBox["Cayleyu", FontColor->RGBColor[0.8, 0.8, 0.4]], "[", "ijk", "]"}], "]"}], "[", \(addPeP[ \(\(nutomass[Last[{t}]] /. addPeP -> Identity\) /. nmrel \) /. {nuu_, ma_} \[RuleDelayed] ma] \), "]"}]}]}], "/.", \(Hold[CompoundExpression] \[Rule] CompoundExpression\)}], "/.", RowBox[{ RowBox[{\(Hold[Condition]\), "[", RowBox[{"a_", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", "b_", "]"}]}], "]"}], "\[Rule]", \(a /; b\)}]}], "/.", \(Hold[Set] \[Rule] Set\)}], "/.", \(Hold[TComment] -> TComment\)}], "/.", \(addPeP -> Identity\)}], "/.", RowBox[{ RowBox[{"Hold", "[", RowBox[{ StyleBox["Cayleyu", FontColor->RGBColor[0.8, 0.8, 0.4]], "[", "ijk__", "]"}], "]"}], "\[Rule]", RowBox[{ StyleBox["Cayleyu", FontColor->RGBColor[0.8, 0.8, 0.4]], "[", "ijk", "]"}]}]}], "/.", RowBox[{ RowBox[{"Hold", "[", RowBox[{ StyleBox["Cayley", FontColor->RGBColor[1, 0.2, 1]], "[", "ijk__", "]"}], "]"}], "\[Rule]", RowBox[{ StyleBox["Cayley", FontColor->RGBColor[1, 0.2, 1]], "[", "ijk", "]"}]}]}], "/.", "\n", "\t\t\t", \(Hold[TA] -> TA\)}], "/.", \({setdel \[RuleDelayed] SetDelayed}\)}], "/.", \(Identity -> identit\)}], "/.", \(identit[a_] -> a\)}]}]}], "]"}]}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{ RowBox[{ RowBox[{"c_.", " ", RowBox[{ StyleBox["TVI", FontColor->RGBColor[0.2, 0.4, 0.8]], "[", "t__", "]"}]}], "==", "rhs_"}], ",", "eqn_String", ",", \(mrel_ : {}\)}], "]"}], ":=", RowBox[{ RowBox[{ StyleBox["Block", FontSize->16, FontWeight->"Bold", FontColor->RGBColor[1, 0.2, 0.2]], "[", RowBox[{\({nm}\), ",", RowBox[{ \(nmrel = Select[Flatten[{mrel}], FreeQ[#1, Factor]&]\), ";", RowBox[{"nmrel", "=", RowBox[{"Join", "[", RowBox[{"nmrel", ",", RowBox[{"{", RowBox[{ RowBox[{\(m\_1\), "\[RuleDelayed]", InterpretationBox[\(m\_1\), m1]}], ",", RowBox[{\(m\_2\), "\[RuleDelayed]", InterpretationBox[\(m\_2\), m2]}], ",", RowBox[{\(m\_3\), "\[RuleDelayed]", InterpretationBox[\(m\_3\), m3]}], ",", RowBox[{\(m\_4\), "\[RuleDelayed]", InterpretationBox[\(m\_4\), m4]}], ",", RowBox[{\(\[CapitalSigma]\_i_\), "\[RuleDelayed]", RowBox[{ StyleBox["ToArgs", FontColor->RGBColor[0.2, 0.6, 1]], "[", \(\[CapitalSigma]\_i\), "]"}]}]}], "}"}]}], "]"}]}], ";", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"HoldForm", "@@", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"setdel", "[", RowBox[{ RowBox[{ RowBox[{"addPeP", "[", RowBox[{ StyleBox["TVR", FontColor->RGBColor[0.2, 0.8, 1]], "@@", \(top/@nutomass[{t}]\)}], "]"}], "/.", "nmrel"}], ",", RowBox[{ \(Hold[CompoundExpression]\), "[", RowBox[{ \(\(Hold[TComment]\)[eqn, \(\(\(addPeP[nutomass[TVR[t]]] /. TVR -> TVIC\) /. {Pattern :> pat, Blank :> blank}\) /. pat[PP, blank[]] :> PP\) /. nmrel]\), "\n", "\t\t\t\t\t\t", ",", RowBox[{ RowBox[{ RowBox[{"Collect", "[", RowBox[{ RowBox[{"TT", "=", RowBox[{"Expand", "[", RowBox[{ "nutonand\[CapitalDelta]u", "[", RowBox[{\(1\/c\), RowBox[{"(", RowBox[{"rhs", "/.", RowBox[{ RowBox[{ StyleBox["TVI", FontColor->RGBColor[0.2, 0.4, 0.8]], "[", "te__", "]"}], "\[RuleDelayed]", RowBox[{"addPeP", "[", RowBox[{"nutomass", "[", RowBox[{ StyleBox["TVI", FontColor->RGBColor[0.2, 0.4, 0.8]], "[", "te", "]"}], "]"}], "]"}]}]}], ")"}]}], "]"}], "]"}]}], ",", RowBox[{ StyleBox["TVI", FontColor->RGBColor[0.2, 0.4, 0.8]], "[", "__", "]"}], ",", \(maybeF[ \((Collect[Numerator[#1], cu[__], Factor]/Collect[Denominator[#1], cu[__], Factor]&)\)/@Factor[#1]]& \)}], "]"}], "/.", "nmrel"}], "/.", \(\[ScriptCapitalC] \[Rule] 1\)}]}], "]"}]}], "]"}], "/.", \(top[i_Integer] \[Rule] i\)}], "/.", \(top \[RuleDelayed] \((patternTest[pattern[#1, blank[]], PQ]&)\)\)}], "/.", RowBox[{ RowBox[{"patternTest", "[", RowBox[{ RowBox[{"pattern", "[", RowBox[{ RowBox[{"dm_", "/;", RowBox[{"MemberQ", "[", RowBox[{ RowBox[{"{", RowBox[{"d", ",", InterpretationBox[\(p\^2\), PP], ",", InterpretationBox[\(m\_1\), m1], ",", InterpretationBox[\(m\_2\), m2], ",", InterpretationBox[\(m\_3\), m3], ",", InterpretationBox[\(m\_4\), m4]}], "}"}], ",", "dm"}], "]"}]}], ",", \(blank[]\)}], "]"}], ",", "_"}], "]"}], "\[RuleDelayed]", \(pattern[dm, blank[]]\)}]}], "/.", \({blank \[RuleDelayed] Blank, pattern \[RuleDelayed] Pattern, patternTest \[RuleDelayed] PatternTest}\)}], "}"}]}], "/.", RowBox[{\(cD[ijk__]\), "\[Rule]", RowBox[{ RowBox[{"Hold", "[", RowBox[{ StyleBox["Cayley", FontColor->RGBColor[1, 0, 0.4]], "[", "ijk", "]"}], "]"}], "[", \(addPeP[ \(nutomass[Last[{t}]] /. nmrel \) /. {nuu_, ma_Symbol} \[RuleDelayed] ma]\), "]"}]}]}], "/.", RowBox[{\(cu[ijk__]\), "\[Rule]", RowBox[{ RowBox[{"Hold", "[", RowBox[{ StyleBox["Cayleyu", FontColor->RGBColor[0.8, 0.8, 0.4]], "[", "ijk", "]"}], "]"}], "[", \(addPeP[ \(nutomass[Last[{t}]] /. nmrel \) /. {nuu_, ma_Symbol} \[RuleDelayed] ma]\), "]"}]}]}], "/.", \(Hold[CompoundExpression] \[Rule] CompoundExpression\)}], "/.", \(Hold[Set] \[Rule] Set\)}], "/.", \(Hold[TComment] -> TComment\)}], "/.", \(addPeP -> Identity\)}], "/.", RowBox[{ RowBox[{"Hold", "[", RowBox[{ StyleBox["Cayleyu", FontColor->RGBColor[0.8, 0.8, 0.4]], "[", "ijk__", "]"}], "]"}], "\[Rule]", RowBox[{ StyleBox["Cayleyu", FontColor->RGBColor[0.8, 0.8, 0.4]], "[", "ijk", "]"}]}]}], "/.", RowBox[{ RowBox[{"Hold", "[", RowBox[{ StyleBox["Cayley", FontColor->RGBColor[1, 0, 0.4]], "[", "ijk__", "]"}], "]"}], "\[Rule]", RowBox[{ StyleBox["Cayley", FontColor->RGBColor[1, 0, 0.4]], "[", "ijk", "]"}]}]}], "/.", \({setdel \[RuleDelayed] SetDelayed}\)}], "/.", \(Identity -> identit\)}], "/.", \(identit[a_] -> a\)}]}]}], "]"}], "/;", RowBox[{\(Head[mrel]\), "=!=", StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]]}]}]}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(c_. \ TJI[t__] == rhs_\), ",", "eqn_String", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", "conds_", "]"}], ",", \(mrel_ : {}\)}], "]"}], ":=", RowBox[{ StyleBox["Block", FontSize->16, FontWeight->"Bold", FontColor->RGBColor[1, 0.2, 0.2]], "[", RowBox[{\({nm, nmrel, \ result}\), ",", RowBox[{ \(\[ScriptCapitalC] = 1\), ";", \(nmrel = Select[Flatten[{mrel}], FreeQ[#1, Factor]&]\), ";", RowBox[{"nmrel", "=", RowBox[{"Join", "[", RowBox[{"nmrel", ",", RowBox[{"{", RowBox[{ RowBox[{\(m\_1\), "\[RuleDelayed]", InterpretationBox[\(m\_1\), m1]}], ",", RowBox[{\(m\_2\), "\[RuleDelayed]", InterpretationBox[\(m\_2\), m2]}], ",", RowBox[{\(m\_3\), "\[RuleDelayed]", InterpretationBox[\(m\_3\), m3]}], ",", RowBox[{\(m\_4\), "\[RuleDelayed]", InterpretationBox[\(m\_4\), m4]}], ",", RowBox[{\(\[CapitalSigma]\_i_\), "\[RuleDelayed]", RowBox[{ StyleBox["ToArgs", FontColor->RGBColor[0.2, 0.6, 1]], "[", \(\[CapitalSigma]\_i\), "]"}]}]}], "}"}]}], "]"}]}], ";", "\n", "\t\t", RowBox[{"result", " ", "=", " ", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"HoldForm", "@@", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"setdel", "[", RowBox[{ \(addPeP[TJR@@\(top/@nutomass[{ tT = t}]\)] /. nmrel\), ",", RowBox[{\(Hold[Condition]\), "[", RowBox[{ \(\(Hold[CompoundExpression]\)[ \(Hold[TComment]\)[eqn, \(\(\(addPeP[nutomass[TJR[t]]] /. TJR -> TJIC\) /. {Pattern :> pat, Blank :> blank}\) /. pat[PP, blank[]] :> PP\) /. nmrel]\t, TJ = \(Collect[TT = Expand[nutonand\[CapitalDelta]u[ \(1\/c\) \((rhs /. TJI[te__] \[RuleDelayed] addPeP[nutomass[TJI[te]]])\)]], TJI[__], maybeF[\((Collect[Numerator[#1], cu[__], Factor]/Collect[Denominator[#1], cu[__], Factor]&)\)/@Factor[#1]]&] /. \[ScriptCapitalC] \[Rule] 1\) /. nmrel]\), ",", RowBox[{ "nutonand\[CapitalDelta]u", "[", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", "conds", "]"}], "]"}]}], "]"}]}], "]"}], "/.", \(top[i_Integer] \[Rule] i\)}], "/.", \(top \[RuleDelayed] \((patternTest[pattern[#1, blank[]], PQ]&)\)\)}], "/.", RowBox[{ RowBox[{"patternTest", "[", RowBox[{ RowBox[{"pattern", "[", RowBox[{ RowBox[{"dm_", "/;", RowBox[{"MemberQ", "[", RowBox[{ RowBox[{"{", RowBox[{"d", ",", InterpretationBox[\(p\^2\), PP], ",", InterpretationBox[\(m\_1\), m1], ",", InterpretationBox[\(m\_2\), m2], ",", InterpretationBox[\(m\_3\), m3], ",", InterpretationBox[\(m\_4\), m4]}], "}"}], ",", "dm"}], "]"}]}], ",", \(blank[]\)}], "]"}], ",", "_"}], "]"}], "\[RuleDelayed]", \(pattern[dm, blank[]]\)}]}], "/.", \({blank \[RuleDelayed] Blank, pattern \[RuleDelayed] Pattern, patternTest \[RuleDelayed] PatternTest}\)}], "}"}]}], "/.", \(HoldPattern[TA[aijk__]] \[Rule] \(\(Hold[TA]\)[aijk]\)[ addPeP[ \(nutomass[Last[{t}]] /. nmrel \) /. {nuu_, ma_} \[RuleDelayed] ma]] \)}], "/.", RowBox[{\(cD[ijk__]\), "\[Rule]", RowBox[{ RowBox[{"Hold", "[", RowBox[{ StyleBox["Cayley", FontColor->RGBColor[1, 0, 0.4]], "[", "ijk", "]"}], "]"}], "[", \(addPeP[ \(nutomass[Last[{t}]] /. nmrel \) /. {nuu_, ma_Symbol} \[RuleDelayed] ma]\), "]"}]}]}], "/.", RowBox[{\(cu[ijk__]\), "\[Rule]", RowBox[{ RowBox[{"Hold", "[", RowBox[{ StyleBox["Cayleyu", FontColor->RGBColor[0.8, 0.8, 0.4]], "[", "ijk", "]"}], "]"}], "[", \(addPeP[ \(nutomass[Last[{t}]] /. nmrel \) /. {nuu_, ma_Symbol} \[RuleDelayed] ma]\), "]"}]}]}], "/.", \(Hold[CompoundExpression] \[Rule] CompoundExpression\)}], "/.", RowBox[{ RowBox[{\(Hold[Condition]\), "[", RowBox[{"a_", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", "b_", "]"}]}], "]"}], "\[Rule]", \(a /; b\)}]}], "/.", \(Hold[Set] \[Rule] Set\)}], "/.", \(Hold[TComment] -> TComment\)}], "/.", RowBox[{ RowBox[{"Hold", "[", RowBox[{ StyleBox["Cayleyu", FontColor->RGBColor[0.8, 0.8, 0.4]], "[", "ijk__", "]"}], "]"}], "\[Rule]", RowBox[{ StyleBox["Cayleyu", FontColor->RGBColor[0.8, 0.8, 0.4]], "[", "ijk", "]"}]}]}], "/.", RowBox[{ RowBox[{"Hold", "[", RowBox[{ StyleBox["Cayley", FontColor->RGBColor[1, 0, 0.4]], "[", "ijk__", "]"}], "]"}], "\[Rule]", RowBox[{ StyleBox["Cayley", FontColor->RGBColor[1, 0, 0.4]], "[", "ijk", "]"}]}]}], "/.", \(Hold[TA] \[Rule] TA\)}], "/.", \({setdel \[RuleDelayed] SetDelayed}\)}]}], ";", \(\[ScriptCapitalC] = . \), ";", " ", "result"}]}], "]"}]}], ";"}]], "Input"], Cell[BoxData[ \(\(SetAttributes[paTT, HoldFirst]; \)\)], "Input"], Cell[BoxData[ RowBox[{ RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{ RowBox[{ RowBox[{"c_.", " ", RowBox[{ StyleBox["TKI", FontColor->RGBColor[0.2, 0.4, 0.8]], "[", "t__", "]"}]}], "==", "rhs_"}], ",", "eqn_String", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", "conds_", "]"}], ",", \(mrel_ : {}\)}], "]"}], ":=", " ", \(\(\(\(MakeFun[c\ TJI[t] == rhs /. TKI -> TJI, eqn, IFF[conds], mrel] /. {PP :> 0, Sqrt[PP] :> 0, Pattern :> paTT}\) /. paTT[0, _] -> 0\) /. paTT -> Pattern\) /. TJIC[d_, li_List] :> TJIC[d, 0, li]\)}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{ RowBox[{ RowBox[{"c_.", " ", RowBox[{ StyleBox["TBI", FontColor->RGBColor[0.2, 0.4, 0.8]], "[", "t__", "]"}]}], "==", "rhs_"}], ",", "eqn_String", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", "conds_", "]"}], ",", \(mrel_ : {}\)}], "]"}], ":=", " ", \(MakeFun[c\ TJI[t] == rhs /. TBI -> TJI, eqn, IFF[conds], mrel] /. { \n\t\t\tTJI :> TBI, TJR :> TBR, TJIC :> TBIC}\)}], ";"}]], "Input"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{ RowBox[{ RowBox[{"c_.", " ", RowBox[{ StyleBox["TAI", FontColor->RGBColor[0.2, 0.4, 0.8]], "[", "t__", "]"}]}], "==", "rhs_"}], ",", "eqn_String", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", "conds_", "]"}], ",", \(mrel_ : {}\)}], "]"}], ":=", " ", \(MakeFun[c\ TJI[t] == rhs /. TAI -> TJI, eqn, IFF[conds], mrel] /. { \n\t\t\tTJI :> TAI, TJR :> TAR, TJIC :> TAIC}\)}], ";"}]], "Input"], Cell[CellGroupData[{ Cell["Interchange", "Subsubsection", CellTags->"T1.5.1.1.1"], Cell[BoxData[ RowBox[{\(Interchange[z_, i_ \[LeftRightArrow] j_]\), ":=", RowBox[{ \(\[Nu]explicit[z] /. {\[Nu]\_i :> \[Nu]\_j, \[Nu]\_j :> \[Nu]\_i, m\_i :> m\_j, m\_j :> m\_i, \[CapitalDelta]\_ij__ :> \((\[CapitalDelta]\_ij /. {i :> j, j :> i})\), u\_ij__ :> \((u\_ij /. {i :> j, j :> i})\), \n\t\t h\_ij__ :> \((h\_ij /. {i :> j, j :> i})\), \[Phi]\_ij__ :> \((\[Phi]\_ij /. {i :> j, j :> i})\), \[Rho]\_ij__ :> \((\[Rho]\_ij /. {i :> j, j :> i})\), \[Sigma]\_ij__ :> \((\[Sigma]\_ij /. {i :> j, j :> i})\), D\_ij__ :> \((D\_ij /. {i :> j, j :> i})\)}\), "/.", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], "[", \(depp__, args_List \), "]"}], ":>", RowBox[{ RowBox[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], "[", \(depp, Sort[args]\), "]"}], "/;", "\[InvisibleSpace]", \(! \((OrderedQ[args])\)\)}]}], ",", "\n", "\t", RowBox[{ RowBox[{ StyleBox["TVI", FontColor->RGBColor[1, 0.6, 0]], "[", \(depp__, args_List \), "]"}], ":>", RowBox[{ RowBox[{ StyleBox["TVI", FontColor->RGBColor[1, 0.6, 0]], "[", \(depp, Sort[args]\), "]"}], "/;", "\[InvisibleSpace]", \(! \((OrderedQ[args])\)\)}]}], ",", "\n", "\t", RowBox[{ RowBox[{ StyleBox["TJI", FontColor->RGBColor[1, 0.6, 0]], "[", \(depp__, args_List \), "]"}], ":>", RowBox[{ RowBox[{ StyleBox["TJI", FontColor->RGBColor[1, 0.6, 0]], "[", \(depp, Sort[args]\), "]"}], "/;", "\[InvisibleSpace]", \(! \((OrderedQ[args])\)\)}]}], ",", "\n", "\t\t\t", RowBox[{ RowBox[{ StyleBox["TBI", FontColor->RGBColor[1, 0.6, 0]], "[", \(depp__, args_List \), "]"}], ":>", RowBox[{ RowBox[{ StyleBox["TBI", FontColor->RGBColor[1, 0.6, 0]], "[", \(depp, Sort[args]\), "]"}], "/;", "\[InvisibleSpace]", \(! \((OrderedQ[args])\)\)}]}]}], "}"}]}]}]], "Input"], Cell[BoxData[ \(\(Interchange[z_, i_ \[LeftRightArrow] j_, vw__] := Interchange[Interchange[z, i \[LeftRightArrow] j], vw]; \)\)], "Input"], Cell[BoxData[ \(\(Interchange[z_, {i_ \[LeftRightArrow] j_}] := Interchange[Interchange[z, i \[LeftRightArrow] j]]; \)\)], "Input"], Cell[BoxData[ \(\(Interchange[z_, {i_ \[LeftRightArrow] j_, vw__}] := Interchange[Interchange[z, i \[LeftRightArrow] j], vw]; \)\)], "Input"], Cell[BoxData[ \(Interchange[ test[\[CapitalDelta]\_\(x, b, y\), \[Nu]\_x, \[Nu]\_y, \[Nu]\_a, \[Nu]\_b, m\_x], \ x \[LeftRightArrow] y, a \[LeftRightArrow] b]\)], "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData["\[Nu]explicit"], "Subsection", CellTags->"T1.5.2.1"], Cell[BoxData[ \(\[Nu]explicit[z_] := \(z /. \[CapitalSigma]\_i_ :> \((Expand[3\ d\ - 2\ - 2\ \(\[Sum]\_\(j = 1\)\%i \[Nu]\_j\)]) \)\) /. \n \t{\t\[Sigma]\_\(i_, j_, k_\) :> \(-\(1\/4\)\) \((d - \[Nu]\_i - 2 \[Nu]\_j)\) \[Phi]\_\(i, j, k\) - \(1\/4\) \((d - 2 \[Nu]\_i - \[Nu]\_j)\) \[Phi]\_\(j, i, k\) - \n\t\t\t\t\t \(1\/4\) \((2 d - 2 \[Nu]\_i - 2 \[Nu]\_j - \[Nu]\_k - 1)\) \[Phi]\_\(k, i, j\), \n\t\t\t h\_\(i_, j_, k_\ \) :> \n\t\t\t\t \(-\(1\/2\)\) \((d - 2 \[Nu]\_j - \[Nu]\_k)\) \(m\_k\^2\) \[Phi]\_\(i, j, k\) - \(1\/2\) \((2 d - \[Nu]\_i - 2 \[Nu]\_j - 2 \[Nu]\_k - 1)\) \(m\_i\^2\) \[Phi]\_\(k, i, j\) + \n\t\t\t\t\t \((d - \[Nu]\_j - 2\ \[Nu]\_k)\) \[Rho]\_\(i, j, k\), \n S\_\(i_, j_, k_\ \) :> \n\t\t\t\t \(-\((d - 2 \[Nu]\_j - \[Nu]\_k)\)\) \(m\_k\^2\) \[Phi]\_\(j, i, k\)\ - \((d - \[Nu]\_j - 2 \[Nu]\_k)\) \(m\_j\^2\) \[Phi]\_\(k, i, j\) + \n\t\t\t\t\t 2 \((2 d - \[Nu]\_i - 2 \[Nu]\_j - 2 \[Nu]\_k - 1)\) \[Rho]\_\(i, j, k\)}\)], "Input"], Cell[CellGroupData[{ Cell["TA", "Subsubsection", CellTags->"T1.5.2.1.1"], Cell[BoxData[ \(MakeBoxes[\(TA[a_, d___Symbol, ijk___Integer]\)[__], fmt_] := SubscriptBox[a, RowBox[{ijk}]]\)], "Input"], Cell[BoxData[ \(MakeBoxes[\(TA[a_, d___Symbol, ijk___Integer, ___Symbol]\)[__], fmt_] := SubscriptBox[a, RowBox[{ijk}]]\)], "Input"], Cell[BoxData[ \(\(\(TA[args__]\)[mar_List] := \((\(TA[args]\)[mar] = \(ta[args]\)[mar])\); \)\)], "Input"], Cell[TextData[{ "Assume that the last argument of {em__} is always p =", Cell[BoxData[ FormBox[ SqrtBox[ RowBox[{" ", FormBox[\(p\^2\), "TraditionalForm"]}]], TraditionalForm]]], "." }], "Text"], Cell["(72)", "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(\(ta[D, i_Integer, j_Integer, k_Integer]\)[{em__}]\), ":=", RowBox[{"With", "[", RowBox[{ \({q = Last[{em}], mi = {em}\[LeftDoubleBracket]i\[RightDoubleBracket], mj = {em}\[LeftDoubleBracket]j\[RightDoubleBracket], mk = {em}\[LeftDoubleBracket]k\[RightDoubleBracket]}\), ",", RowBox[{"Factor", "[", RowBox[{ \(q\^8\), "-", \(4\ q\^6\ \((mi\^2 + mj\^2 + mk\^2)\)\), "+", \(q\^4\ \(( 6\ \((mi\^4 + mj\^4 + mk\^4)\) + 4\ \((mi\^2\ mj\^2 + mk\^2\ mi\^2 + mk\^2\ mj\^2)\)) \)\), "-", \(4\ q\^2\ \((mi\^6 + mj\^6 + mk\^6 - mi\^2\ \((mj\^4 + mk\^4)\) - mj\^2\ \((mi\^4 + mk\^4)\) - mk\^2\ \((mi\^4 + mj\^4)\) + 10\ mi\^2\ mj\^2\ mk\^2) \)\), "+", SuperscriptBox[ RowBox[{ RowBox[{ StyleBox["Cayley", FontColor->RGBColor[1, 0, 0.4]], "[", \(i, j, k\), "]"}], "[", \({em}\), "]"}], "2"]}], "]"}]}], "]"}]}], ";"}]], "Input"], Cell["(73)", "Text"], Cell[BoxData[ \(\(\(ta[\[Rho], i_Integer, j_Integer, k_Integer]\)[{em__}] := With[{q = Last[{em}], mi = {em}\[LeftDoubleBracket]i\[RightDoubleBracket], mj = {em}\[LeftDoubleBracket]j\[RightDoubleBracket], mk = {em}\[LeftDoubleBracket]k\[RightDoubleBracket]}, Factor[\(-q\^6\) + 3\ q\^4\ \((mi\^2 + mj\^2 + mk\^2)\) - q\^2\ \(( 3\ \((mi\^4 + mj\^4 + mk\^4)\) + 2\ \((mi\^2\ mj\^2 + mk\^2\ mi\^2 + mk\^2\ mj\^2)\))\) + \ \((mi\^6 + mj\^6 + mk\^6 - mi\^2\ \((mj\^4 + mk\^4)\) - mj\^2\ \((mi\^4 + mk\^4)\) - mk\^2\ \((mi\^4 + mj\^4)\) + 10\ mi\^2\ mj\^2\ mk\^2)\)]]; \)\)], "Input"], Cell["(74)", "Text"], Cell[BoxData[ \(\(\(ta[\[Phi], i_Integer, j_Integer, k_Integer]\)[{em__}] := With[{q = Last[{em}], mi = {em}\[LeftDoubleBracket]i\[RightDoubleBracket], mj = {em}\[LeftDoubleBracket]j\[RightDoubleBracket], mk = {em}\[LeftDoubleBracket]k\[RightDoubleBracket]}, 4 Factor[ q\^4\ + 2 \( q\^2\) \((mi\^2 - mj\^2 - mk\^2)\) + \((mj\^2 - mk\^2)\)\^2 + \(mi\^2\) \((2 mj\^2 + 2 mk\^2 - 3 mi\^2)\)]]; \)\)], "Input"], Cell["(75)", "Text"], Cell[BoxData[ \(\(\(ta[\[Sigma], d_, i_Integer, j_Integer, k_Integer, \[Nu]i_Integer, \[Nu]j_Integer, \[Nu]k_Integer]\)[{em__}] := Factor[\(-\(1\/4\)\) \((d - \[Nu]i - 2 \[Nu]j)\) \(TA[\[Phi], i, j, k]\)[{em}]\ - \(1\/4\) \((d - 2 \[Nu]i - \[Nu]j)\) \(TA[\[Phi], j, i, k]\)[{em}] - \(1\/4\) \((2 d - 2 \[Nu]i - 2 \[Nu]j - \[Nu]k - 1)\) \(TA[\[Phi], k, i, j]\)[{em}]\ \ \ ]; \)\)], "Input"], Cell["(76)", "Text"], Cell[BoxData[ \(\(\(ta[h, d_, i_Integer, j_Integer, k_Integer, \[Nu]i_Integer, \[Nu]j_Integer, \[Nu]k_Integer]\)[{em__}] := \n\t With[{q = Last[{em}], mi = {em}\[LeftDoubleBracket]i\[RightDoubleBracket], mj = {em}\[LeftDoubleBracket]j\[RightDoubleBracket], mk = {em}\[LeftDoubleBracket]k\[RightDoubleBracket]}, Factor[\(-\(1\/2\)\) \((d - 2 \[Nu]j - \[Nu]k)\) \(mk\^2\) \(TA[\[Phi], i, j, k]\)[{em}] - \(1\/2\) \((2 d - \[Nu]i - 2 \[Nu]j - 2 \[Nu]k - 1)\) \(mi\^2\) \(TA[\[Phi], k, i, j]\)[{em}] + \((d - \[Nu]j - 2\ \[Nu]k)\) \(TA[\[Rho], i, j, k]\)[{em}]\ \ \ ]]; \)\)], "Input"], Cell["(79)", "Text"], Cell[BoxData[ RowBox[{ RowBox[{ \(\(ta[S, d_, i_Integer, j_Integer, k_Integer, \[Nu]i_Integer, \[Nu]j_Integer, \[Nu]k_Integer]\)[{em__}]\), ":=", "\n", "\t\t", RowBox[{"With", "[", RowBox[{ \({q = Last[{em}], mi = {em}\[LeftDoubleBracket]i\[RightDoubleBracket], mj = {em}\[LeftDoubleBracket]j\[RightDoubleBracket], mk = {em}\[LeftDoubleBracket]k\[RightDoubleBracket]}\), ",", RowBox[{"Factor", "[", RowBox[{ \(\(-\((d - 2 \[Nu]j - \[Nu]k)\)\) \(mk\^2\) \(TA[\[Phi], j, i, k]\)[{em}]\), " ", "-", RowBox[{ \((d - \[Nu]j - 2 \[Nu]k)\), \(mj\^2\), \(\(TA[\[Phi], k, i, j]\)[{em}]\), "test", "\n", FormBox["test", "TraditionalForm"], "2", \((2 d - \[Nu]i - 2 \[Nu]j - 2 \[Nu]k - 1)\), \(\(TA[\[Rho], i, j, k]\)[{em}]\)}]}], " ", "]"}]}], "]"}]}], ";"}]], "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["CheckRecursion", "Subsection", CellTags->"T1.5.3.1"], Cell["\<\ The following functions check the recurrence relations for J and V (using the \ final form as generated by MakeFun) via their Mellin-Integral Kernels.\ \>", "Text"], Cell["\<\ This test is applicable in the general case and if some of the masses vanish, but not for other special cases !!!\ \>", "Text"], Cell[CellGroupData[{ Cell["CheckTVIRecursion", "Subsubsection", CellTags->"T1.5.3.1.1"], Cell[BoxData[ \(\(TVIKernel[d_, PP, \ lis_] := \n \(\(\((\(-PP\))\)\^\(d - n1 - n2 - n3 - n4\)\) \(\((m1\^2\/\(-PP\))\)\^s1\) \(\((m2\^2\/\(-PP\))\)\^s2\) \(\((m3\^2\/\(-PP\))\)\^s3\) \((m4\^2\/\(-PP\))\)\^s4\)* TVIpsi\ [d, \ \((lis /. {m1 -> s1, m2 -> s2, m3 -> s3, m4 -> s4})\)]; \)\)], "Input"], Cell[BoxData[ \(\(TVIPsi[d_, \n \t{{n1_, \ s1_}, \ {n2_, s2_}, {n3_, s3_}, {n4_, s4_}}] := \(\((\(-1\))\)\^\(n1 + n2 + n3 + n4 + 1\)\) \(\(gamma[\(-s1\)] gamma[d/2 - n1 - s1]\)\/gamma[n1]\) \(\(gamma[\(-s2\)] gamma[d/2 - n2 - s2]\)\/gamma[n2]\) \(\(gamma[\(-s3\)] gamma[d/2 - n3 - s3]\)\/gamma[n3]\) \(\(gamma[\(-s4\)] gamma[n4 + s4]\)\/gamma[n4]\) gamma[n1 + n2 + n3 + n4 + s1 + s2 + s3 + s4 - d]/ gamma[3 d/2 - n1 - n2 - n3 - n4 - s1 - s2 - s3 - s4] \(gamma[n1 + n3 + s1 + s3 - d/2]\/gamma[ n1 + n3 + n4 + s1 + s3 + s4 - d/2]\) gamma[d - n1 - n3 - n4 - s1 - s3 - s4]\/gamma[d - n1 - n3 - s1 - s3]; \)\)], "Input"], Cell[BoxData[ \(CheckTVIRecursion[expr_] := \ If[\ $CheckRecursion === True, \n\t Block[{rel, kern, \ nkern}, \n rel = \(( \((Extract[expr /. TVIC -> TVIkernel, {1, 2, 1, 1, 2}])\) - Extract[expr /. TVI -> TVIkernel, {1, 2, 1, 2}])\); \n If[\ {TVIkernel} === Union[Head/@ Cases[rel, ff_[__] /; Context[ff] =!= "\", 4]], \t \nrel = Collect[Numerator[Together[rel]], \ TVI[__], Factor]; \n kern = rel /. TVIkernel -> TVIKernel; \n kern = kern /. {PP -> \(-1\), m1 -> Sqrt[z1], m2 -> Sqrt[z2], m3 -> Sqrt[z3], m4 -> Sqrt[z4]}; \n kern = PowerExpand[kern]; \nkern = Expand[kern]; \n kern = kern /. { \(z1\^\(s1 + w1_. \)\) \(z2\^\(s2 + w2_. \)\) \(z3\^\(s3 + w3_. \)\) \(z4\^\(s4 + w4_. \)\) fac_ :> \((fac /. {s1 -> s1 - w1, s2 -> s2 - w2, s3 -> s3 - w3, s4 -> s4 - w4})\)}\ ; \n kern = \(\(kern /. TVIpsi -> TVIPsi\) /. { gamma[zz_] :> gamma[Expand[zz]]}\) /. { gamma[zz_ + nn_Integer] :> gamma[zz] Pochhammer[zz, nn]}; \n \t\t\t\tKERN = kern; \nkern = kern /. {gamma[zz_] :> 1}; \n kern = \(kern /. { \((\(-1\))\)\^\(nn_ + ww_Integer\) :> \((\(-1\))\)\^ww} \) /. {\((\(-1\))\)\^nn_ :> 1}; \n nkern = Table[\n\t\t\t kern /. Thread[{d, \ n1, \ n2, \ n3, n4, s1, s2, \ s3, s4} -> Table[Random[], {9}]], {3}]; \nnkern\ \ , \n\t\t Print["\"]\ ]\ ], \n\t\tPrint["\"]]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["CheckTJIRecursion", "Subsubsection", CellTags->"T1.5.3.2.1"], Cell[BoxData[ \(\(TJIKernel[d_, PP, \ lis_] := \n \(\((\(-PP\))\)\^\(d - n1 - n2 - n3\)\) \(\((m1\^2\/\(-PP\))\)\^s1\) \(\((m2\^2\/\(-PP\))\)\^s2\) \((m3\^2\/\(-PP\))\)\^s3* TJIpsi\ [d, \ \((lis /. {m1 -> s1, m2 -> s2, m3 -> s3})\)]; \)\)], "Input"], Cell[BoxData[ \(TJIPsi\ [d_, {{n1_, \ s1_}, \ {n2_, s2_}, {n3_, s3_}}] := Evaluate[TVIPsi[d, \n\t{{n1, \ s1}, \ {n2, s2}, {n3, s3}, {0, 0}}]/ gamma[0]]\)], "Input"], Cell[BoxData[ \(Clear[CheckTJIRecursion]; \n CheckTJIRecursion[expr_] := \ If[\ $CheckRecursion === True, \n\t Block[{rel, kern, nkern}, \n rel = \(( \((Extract[expr /. TJIC -> TJIkernel, {1, 2, 1, 1, 2}])\) - Extract[expr /. TJI -> TJIkernel, {1, 2, 1, 2}])\); \n\t\t\t REL = rel; \t\t\t\n If[{TJIkernel} === Union[Head/@ Cases[rel, ff_[__] /; Context[ff] =!= "\", 4]]\ , \t\t\t\nrel = Collect[Numerator[Together[rel]], \ TJI[__], Factor]; \n kern = rel /. TJIkernel -> TJIKernel; \n kern = kern /. {PP -> \(-1\), m1 -> Sqrt[z1], m2 -> Sqrt[z2], m3 -> Sqrt[z3]}; \nkern = PowerExpand[kern]; \n kern = Expand[kern]; \n kern = kern /. { \(z1\^\(s1 + w1_. \)\) \(z2\^\(s2 + w2_. \)\) \(z3\^\(s3 + w3_. \)\) fac_ :> \((fac /. {s1 -> s1 - w1, s2 -> s2 - w2, s3 -> s3 - w3}) \)}; \ \n kern = \(\(kern /. TJIpsi -> TJIPsi\) /. { gamma[zz_] :> gamma[Expand[zz]]}\) /. { gamma[zz_ + nn_Integer] :> gamma[zz] Pochhammer[zz, nn]}; \n \ \ \ \ \ \ KERN = kern; \nkern = kern /. {gamma[zz_] :> 1}; \n kern = \(kern /. { \((\(-1\))\)\^\(nn_ + ww_Integer\) :> \((\(-1\))\)\^ww} \) /. {\((\(-1\))\)\^nn_ :> 1}; \n nkern = Table[\n\t\t\t kern /. Thread[{d, \ n1, \ n2, \ n3, s1, s2, \ s3} -> Table[Random[], {7}]], {3}]; \nnkern\ \ , \n\t\t Print["\"]\ ]\ ], \n\t\tPrint["\"]]\)], "Input"] }, Closed]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Recurrence Relations Input and Recursion Function Generation", "Section", CellDingbat->"\[FilledSmallCircle]", CellTags->"T1.6.1"], Cell[TextData[{ "Most ", Cell[BoxData[ \(TraditionalForm\`e\_\( ... \ \)\)]], "equations below were entered by the palettes which show up when \ $PutPalettes is set to True.\nExamples of alternative (hand) input are (50) \ , (201) -- (205)." }], "Text"], Cell[CellGroupData[{ Cell["Input (35)", "Subsection", CellTags->"T1.6.1.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_35\), "=", "\n", RowBox[{ RowBox[{"2", \(\[Nu]\_1\), "\[ScriptCapitalC]", " ", InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["F", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"], FormBox[\(\[Nu]\_5\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TFI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4], Subscript[ \[Nu], 5]}], Editable->True]}], "\[Equal]", " ", RowBox[{ RowBox[{"(", RowBox[{ \(\((d - 2 \[Nu]\_1 - \[Nu]\_3 - \[Nu]\_5)\) \[CapitalDelta]\_1\), "+", RowBox[{\(\[CapitalDelta]\_\(3, 4, 5\)\), RowBox[{"(", RowBox[{ RowBox[{\(\[Nu]\_5\), InterpretationBox[ StyleBox[\(5\^+\), FontWeight->"Bold"], Schiebe[ 5, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True]}], ")"}]}], "-", RowBox[{\(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True], InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True]}]}], ")"}]}], "+", RowBox[{\(\[CapitalDelta]\_2\), RowBox[{"(", RowBox[{ RowBox[{\(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(5\^-\), FontWeight->"Bold"], Schiebe[ 5, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}], ")"}]}], "+", RowBox[{\(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(5\^-\), FontWeight->"Bold"], Schiebe[ 5, "-"]], "-", InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True]}], ")"}]}], "+", \(\[Nu]\_5\), "-", \(\[Nu]\_1\)}], ")"}]}], "+", "\n", "\t\t\t\t", RowBox[{\(\[CapitalDelta]\_6\), RowBox[{"(", RowBox[{ RowBox[{\(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}], "+", RowBox[{\(\[Nu]\_5\), InterpretationBox[ StyleBox[\(5\^+\), FontWeight->"Bold"], Schiebe[ 5, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True]}], ")"}]}], "+", \(\[Nu]\_3\), "-", \(\[Nu]\_1\)}], ")"}]}]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["F", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"], FormBox[\(\[Nu]\_5\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TFI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4], Subscript[ \[Nu], 5]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_35 = OperatorApplyF[e\_35]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (35)", "Subsection", CellTags->"T1.6.2.1"], Cell[BoxData[ \(h\_351 = s\_35 /. \[Nu]\_1 -> \((\[Nu]\_1 - 1)\)\)], "Input"], Cell[CellGroupData[{ Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`1\^\(+\ \)\)]], " (35_1)" }], "Subsubsection", CellTags->"T1.6.2.1.1"], Cell[BoxData[ RowBox[{\(f\_351\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_351\), ",", "\"\<(35_1)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", RowBox[{\(\[Nu]\_1 > 1\), "&&", RowBox[{ RowBox[{ StyleBox["Cayley", FontColor->RGBColor[1, 0, 0.4]], "[", RowBox[{ InterpretationBox[\(m\_1\), m1], ",", InterpretationBox[\(m\_2\), m2], ",", InterpretationBox[\(m\_3\), m3], ",", InterpretationBox[\(m\_4\), m4], ",", InterpretationBox[\(m\_5\), m5], ",", SqrtBox[ InterpretationBox[\(p\^2\), PP]]}], "]"}], "=!=", "0"}]}], "]"}]}], "]"}]}]], "Input"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`2\^\(+\ \)\)]], " (35_2)" }], "Subsubsection", CellTags->"T1.6.2.2.1"], Cell[BoxData[ RowBox[{\(f\_352\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{ \(Interchange[h\_351, 1 \[LeftRightArrow] 2, 3 \[LeftRightArrow] 4] \), ",", "\"\<(35_2)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", RowBox[{\(\[Nu]\_2 > 1\), "&&", RowBox[{ RowBox[{ StyleBox["Cayley", FontColor->RGBColor[1, 0, 0.4]], "[", RowBox[{ InterpretationBox[\(m\_1\), m1], ",", InterpretationBox[\(m\_2\), m2], ",", InterpretationBox[\(m\_3\), m3], ",", InterpretationBox[\(m\_4\), m4], ",", InterpretationBox[\(m\_5\), m5], ",", SqrtBox[ InterpretationBox[\(p\^2\), PP]]}], "]"}], "=!=", "0"}]}], "]"}]}], "]"}]}]], "Input"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`3\^\(+\ \)\)]], " (35_3)" }], "Subsubsection", CellTags->"T1.6.2.3.1"], Cell[BoxData[ RowBox[{\(f\_353\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{ \(Interchange[h\_351, 1 \[LeftRightArrow] 3, 2 \[LeftRightArrow] 4] \), ",", "\"\<(35_3)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", RowBox[{\(\[Nu]\_3 > 1\), "&&", RowBox[{ RowBox[{ StyleBox["Cayley", FontColor->RGBColor[1, 0, 0.4]], "[", RowBox[{ InterpretationBox[\(m\_1\), m1], ",", InterpretationBox[\(m\_2\), m2], ",", InterpretationBox[\(m\_3\), m3], ",", InterpretationBox[\(m\_4\), m4], ",", InterpretationBox[\(m\_5\), m5], ",", SqrtBox[ InterpretationBox[\(p\^2\), PP]]}], "]"}], "=!=", "0"}]}], "]"}]}], "]"}]}]], "Input"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`4\^\(+\ \)\)]], " (35_4)" }], "Subsubsection", CellTags->"T1.6.2.4.1"], Cell[BoxData[ RowBox[{\(f\_354\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{ \(Interchange[h\_351, 1 \[LeftRightArrow] 4, 2 \[LeftRightArrow] 3] \), ",", "\"\<(35_4)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", RowBox[{\(\[Nu]\_4 > 1\), "&&", RowBox[{ RowBox[{ StyleBox["Cayley", FontColor->RGBColor[1, 0, 0.4]], "[", RowBox[{ InterpretationBox[\(m\_1\), m1], ",", InterpretationBox[\(m\_2\), m2], ",", InterpretationBox[\(m\_3\), m3], ",", InterpretationBox[\(m\_4\), m4], ",", InterpretationBox[\(m\_5\), m5], ",", SqrtBox[ InterpretationBox[\(p\^2\), PP]]}], "]"}], "=!=", "0"}]}], "]"}]}], "]"}]}]], "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Input (3501)", "Subsection", CellTags->"T1.6.3.1"], Cell[BoxData[ \(Cayley[m1, m5, m5, m4, m5, m5] // Factor\)], "Input"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`m\_1 = 0\ \ ; \ \ m\_2 = \(m\_3 = m\_5\); \ \ \ p\^2 = m\_5\%2\)]]], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_3501\), "=", RowBox[{ RowBox[{\((d - 2 \[Nu]\_1 - \[Nu]\_3 - \[Nu]\_5)\), InterpretationBox[ SubsuperscriptBox[ StyleBox["F", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"], FormBox[\(\[Nu]\_5\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TFI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4], Subscript[ \[Nu], 5]}], Editable->True]}], "==", RowBox[{ RowBox[{"(", " ", RowBox[{ RowBox[{\(\[Nu]\_5\), RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}], ")"}], InterpretationBox[ StyleBox[\(5\^+\), FontWeight->"Bold"], Schiebe[ 5, "+"], Editable->True]}], "+", RowBox[{\(\[Nu]\_3\), InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True], InterpretationBox[ RowBox[{ StyleBox[\(3\^+\), FontWeight->"Bold"], " "}], Schiebe[ 3, "+"], Editable->True]}]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["F", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"], FormBox[\(\[Nu]\_5\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TFI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4], Subscript[ \[Nu], 5]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_3501 = OperatorApplyF[e\_3501]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "MakeFun (3501) \[CapitalDelta]=0 ", Cell[BoxData[ \(TraditionalForm\`\((p\^2 = m\^2)\)\)]] }], "Subsection", CellTags->"T1.6.4.1"], Cell[BoxData[ \(h\_3501 = s\_3501\)], "Input"], Cell[BoxData[ RowBox[{\(f\_3501\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(s\_3501\), ",", "\"\<(3501)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", \(PP === m5^2\), "]"}], ",", \({m1 :> 0, m2 :> m5, m3 :> m5}\)}], "]"}]}]], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (3502)", "Subsection", CellTags->"T1.6.5.1"], Cell[BoxData[ \(Cayley[m1, m5, m5, m4, m5, m5] // Factor\)], "Input"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`m\_4 = 0\ \ ; \ \ m\_2 = \(m\_3 = m\_5\); \ \ \ p\^2 = m\_5\%2\)]]], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_3502\), "=", RowBox[{ RowBox[{\((d - 2 \[Nu]\_1 - \[Nu]\_3 - \[Nu]\_5)\), InterpretationBox[ SubsuperscriptBox[ StyleBox["F", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"], FormBox[\(\[Nu]\_5\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TFI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4], Subscript[ \[Nu], 5]}], Editable->True]}], "==", RowBox[{ RowBox[{"(", " ", RowBox[{ RowBox[{\(\[Nu]\_5\), RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}], ")"}], InterpretationBox[ StyleBox[\(5\^+\), FontWeight->"Bold"], Schiebe[ 5, "+"], Editable->True]}], "+", RowBox[{\(\[Nu]\_3\), InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True], InterpretationBox[ RowBox[{ StyleBox[\(3\^+\), FontWeight->"Bold"], " "}], Schiebe[ 3, "+"], Editable->True]}]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["F", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"], FormBox[\(\[Nu]\_5\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TFI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4], Subscript[ \[Nu], 5]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_3502 = OperatorApplyF[e\_3502]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "MakeFun (3502) \[CapitalDelta]=0 ", Cell[BoxData[ \(TraditionalForm\`\((p\^2 = m\^2)\)\)]] }], "Subsection", CellTags->"T1.6.6.1"], Cell[BoxData[ \(h\_3502 = s\_3502\)], "Input"], Cell[BoxData[ RowBox[{\(f\_3502\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_3502\), ",", "\"\<(3502)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", \(PP === m5^2\), "]"}], ",", \({m4 :> 0, m2 :> m5, m3 :> m5}\)}], "]"}]}]], "Input"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "MakeFun (3503) \[CapitalDelta]=0 ", Cell[BoxData[ \(TraditionalForm\`\((p\^2 = m\^2)\)\)]] }], "Subsection", CellTags->"T1.6.7.1"], Cell[BoxData[ \(Cayley[m5, 0, m3, m5, m5, m5]\)], "Input"], Cell[BoxData[ \(h\_3503 = Interchange[s\_3502, 1 \[LeftRightArrow] 2, \ 3 \[LeftRightArrow] 4] \)], "Input"], Cell[BoxData[ RowBox[{\(f\_3503\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_3503\), ",", "\"\<(3503)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", \(PP === m5^2\), "]"}], ",", \({m2 :> 0, m1 :> m5, m4 :> m5}\)}], "]"}]}]], "Input"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "MakeFun (3504) \[CapitalDelta]=0 ", Cell[BoxData[ \(TraditionalForm\`\((p\^2 = m\^2)\)\)]] }], "Subsection", CellTags->"T1.6.8.1"], Cell[BoxData[ \(Cayley[m5, m2, 0, m5, m5, m5]\)], "Input"], Cell[BoxData[ \(h\_3504 = Interchange[s\_3502, 1 \[LeftRightArrow] 3, \ 2 \[LeftRightArrow] 4] \)], "Input"], Cell[BoxData[ RowBox[{\(f\_3504\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_3504\), ",", "\"\<(3504)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", \(PP === m5^2\), "]"}], ",", \({m3 :> 0, m1 :> m5, m4 :> m5}\)}], "]"}]}]], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (41)", "Subsection", CellTags->"T1.6.9.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_41\), "=", "\n", RowBox[{ RowBox[{"2", \(\[Nu]\_5\), " ", "\[ScriptCapitalC]", " ", InterpretationBox[ StyleBox[\(5\^+\), FontWeight->"Bold"], Schiebe[ 5, "+"]], InterpretationBox[ SubsuperscriptBox[ StyleBox["F", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"], FormBox[\(\[Nu]\_5\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TFI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4], Subscript[ \[Nu], 5]}]]}], " ", "\[Equal]", " ", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{\(\[CapitalDelta]\_\(1, 3, 6\)\), RowBox[{"(", RowBox[{ RowBox[{\(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"]], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"]], "-", InterpretationBox[ StyleBox[\(5\^-\), FontWeight->"Bold"], Schiebe[ 5, "-"]]}], ")"}]}], "+", RowBox[{\(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"]], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"]], "-", InterpretationBox[ StyleBox[\(5\^-\), FontWeight->"Bold"], Schiebe[ 5, "-"]]}], ")"}]}]}], ")"}]}], "+", \(\((d - \[Nu]\_1 - \[Nu]\_3 - 2 \[Nu]\_5)\) \[CapitalDelta]\_5\), "+", RowBox[{\(\[CapitalDelta]\_2\), RowBox[{"(", RowBox[{ RowBox[{\(\[Nu]\_5\), InterpretationBox[ StyleBox[\(5\^+\), FontWeight->"Bold"], Schiebe[ 5, "+"]], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"]], "-", InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"]]}], ")"}]}], "+", RowBox[{\(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"]], InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"]]}], "+", \(\[Nu]\_1\), "-", \(\[Nu]\_5\)}], ")"}]}], "+", RowBox[{\(\[CapitalDelta]\_4\), RowBox[{"(", RowBox[{ RowBox[{\(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"]], InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"]]}], "+", RowBox[{\(\[Nu]\_5\), InterpretationBox[ StyleBox[\(5\^+\), FontWeight->"Bold"], Schiebe[ 5, "+"]], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"]], "-", InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"]]}], ")"}]}], "+", \(\[Nu]\_3\), "-", \(\[Nu]\_5\)}], ")"}]}]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["F", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"], FormBox[\(\[Nu]\_5\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TFI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4], Subscript[ \[Nu], 5]}]]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_41 = OperatorApplyF[e\_41]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (41)", "Subsection", CellTags->"T1.6.10.1"], Cell[BoxData[ \(h\_41 = s\_41 /. \[Nu]\_5 \[Rule] \[Nu]\_5 - 1\)], "Input"], Cell[BoxData[ RowBox[{\(f\_41\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_41\), ",", "\"\<(41)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", RowBox[{\(\[Nu]\_5 > 1\), "&&", RowBox[{ RowBox[{ StyleBox["Cayley", FontColor->RGBColor[1, 0, 0.4]], "[", RowBox[{ InterpretationBox[\(m\_1\), m1], ",", InterpretationBox[\(m\_2\), m2], ",", InterpretationBox[\(m\_3\), m3], ",", InterpretationBox[\(m\_4\), m4], ",", InterpretationBox[\(m\_5\), m5], ",", SqrtBox[ InterpretationBox[\(p\^2\), PP]]}], "]"}], "=!=", "0"}]}], "]"}]}], "]"}]}]], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (43)", "Subsection", CellTags->"T1.6.11.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(p\^2\)]], " and ( ", Cell[BoxData[ \(TraditionalForm\`m\_5\%2 == 0\)]], " && ", Cell[BoxData[ \(TraditionalForm\`m\_1\%2\)]], "==", Cell[BoxData[ \(TraditionalForm\`m\_2\%2\)]], " && ", Cell[BoxData[ \(TraditionalForm\`m\_3\%2\)]], "== ", Cell[BoxData[ \(TraditionalForm\`m\_4\%2\)]], " ) \[DoubleLongRightArrow] \[CapitalDelta] == 0" }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_43\), "=", RowBox[{ RowBox[{\((d - \[Nu]\_1 - \[Nu]\_3 - 2 \[Nu]\_5)\), InterpretationBox[ SubsuperscriptBox[ StyleBox["F", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"], FormBox[\(\[Nu]\_5\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TFI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4], Subscript[ \[Nu], 5]}], Editable->True]}], "\[Equal]", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{\(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(5\^-\), FontWeight->"Bold"], Schiebe[ 5, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}], ")"}]}], "+", RowBox[{\(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(5\^-\), FontWeight->"Bold"], Schiebe[ 5, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True]}], ")"}]}]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["F", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"], FormBox[\(\[Nu]\_5\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TFI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4], Subscript[ \[Nu], 5]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_43 = OperatorApplyF[e\_43]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (44)", "Subsection", CellTags->"T1.6.12.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(p\^2\)]], " and ( ", Cell[BoxData[ \(TraditionalForm\`m\_5\%2 == 0\)]], " && ", Cell[BoxData[ \(TraditionalForm\`m\_1\%2\)]], "==", Cell[BoxData[ \(TraditionalForm\`m\_2\%2\)]], " && ", Cell[BoxData[ \(TraditionalForm\`m\_3\%2\)]], "== ", Cell[BoxData[ \(TraditionalForm\`m\_4\%2\)]], " ) \[DoubleLongRightArrow] \[CapitalDelta] == 0" }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_44\), "=", RowBox[{ RowBox[{\((d - \[Nu]\_2 - \[Nu]\_4 - 2 \[Nu]\_5)\), InterpretationBox[ SubsuperscriptBox[ StyleBox["F", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"], FormBox[\(\[Nu]\_5\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TFI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4], Subscript[ \[Nu], 5]}], Editable->True]}], "\[Equal]", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{\(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(5\^-\), FontWeight->"Bold"], Schiebe[ 5, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True]}], ")"}]}], "+", RowBox[{\(\[Nu]\_4\), InterpretationBox[ StyleBox[\(4\^+\), FontWeight->"Bold"], Schiebe[ 4, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(5\^-\), FontWeight->"Bold"], Schiebe[ 5, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}], ")"}]}]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["F", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"], FormBox[\(\[Nu]\_5\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TFI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4], Subscript[ \[Nu], 5]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_44 = OperatorApplyF[e\_44]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (45)", "Subsection", CellTags->"T1.6.13.1"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_45\), "=", " ", RowBox[{ RowBox[{\(\[CapitalDelta]\_\(1, 3, 6\)\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["F", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"], FormBox[\(\[Nu]\_5\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TFI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4], Subscript[ \[Nu], 5]}], Editable->True]}], "\[Equal]", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{\(u\_\(6, 1, 3\)\), RowBox[{"(", RowBox[{ RowBox[{\(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}], "+", RowBox[{\(\[Nu]\_5\), InterpretationBox[ StyleBox[\(5\^+\), FontWeight->"Bold"], Schiebe[ 5, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True]}], ")"}]}]}], ")"}]}], "-", RowBox[{"2", \(u\_\(1, 3, 6\)\), RowBox[{"(", " ", RowBox[{ RowBox[{\(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(5\^-\), FontWeight->"Bold"], Schiebe[ 5, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True]}], ")"}]}], "+", " ", RowBox[{\(\[Nu]\_4\), InterpretationBox[ StyleBox[\(4\^+\), FontWeight->"Bold"], Schiebe[ 4, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(5\^-\), FontWeight->"Bold"], Schiebe[ 5, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}], ")"}]}], "+", \(-\[CapitalSigma]\_5\), "-", \(\[Nu]\_1\), "+", \(3 \[Nu]\_3\)}], ")"}]}], "+", RowBox[{"2", \(m\_3\%2\), RowBox[{"(", RowBox[{ RowBox[{\(\[Nu]\_5\), InterpretationBox[ StyleBox[\(5\^+\), FontWeight->"Bold"], Schiebe[ 5, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}], ")"}]}], "+", RowBox[{\(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True], InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True]}], "+", \(\[Nu]\_1\), "-", \(\[Nu]\_3\)}], ")"}]}]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["F", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"], FormBox[\(\[Nu]\_5\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TFI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4], Subscript[ \[Nu], 5]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_45 = OperatorApplyF[e\_45]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (43) and (44)", "Subsection", CellTags->"T1.6.14.1"], Cell[BoxData[ \(f\_43 = MakeFun[s\_43, "\<(43)\>", IFF[\[Nu]\_1 + \[Nu]\_3 + 2 \[Nu]\_5 - \((d /. dd_Symbol :> 4)\) =!= 0], {m5 :> 0, m4 :> m3, m2 :> m1}]\)], "Input"], Cell[BoxData[ \(f\_44 = MakeFun[s\_44, "\<(44)\>", {m5 :> 0, m4 :> m3, m2 :> m1}]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (50)", "Subsection", CellTags->"T1.6.15.1"], Cell["\<\ Subscript[f, 50] = HoldForm[TFR[d_, PP_, {{(n1_)?PQ, m1_}, {(n2_)?PQ, m2_}, {(n3_)?PQ, m3_}, {(n4_)?PQ, m4_}, {(n5_)?PQ, m5_}}] := (TComment[\"(50)\", TFIC[d, PP, {{n1, m1}, {n2, m2}, {n3, m3}, {n4, m4}, {n5, m5}}]]; Block[{r1 = 3 - d, r2 = 4 - d, r3 = -(m1^2*m2^2*m3^2) + m2^4*m3^2 + m2^2*m3^4 + m1^4*m4^2 - m1^2*m2^2*m4^2 - m1^2*m3^2*m4^2 - m2^2*m3^2*m4^2 + m1^2*m4^4 + m1^2*m2^2*m5^2 - m2^2*m3^2*m5^2 - m1^2*m4^2*m5^2 + m3^2*m4^2*m5^2 + m1^2*m3^2*PP - m2^2*m3^2*PP - m1^2*m4^2*PP + m2^2*m4^2*PP - m1^2*m5^2*PP - m2^2*m5^2*PP - m3^2*m5^2*PP - m4^2*m5^2*PP + m5^4*PP + m5^2*PP^2, r4 = -4 + d, r5 = -3 + d, r6 = -7 + 2*d, r7 = -(m2^2*r4) + m3^2*r5 - m5^2*r5 + m4^2*r6, r8 = -10 + 3*d, r9 = -m3^2 + m4^2, r10 = -11 + 3*d, r11 = -(m4^2*r10) - 3*m5^2*r5 + m3^2*r6, r12 = m2^2*r11 + m5^4*r5 + m2^4*r8 + m4^2*r4*r9 + m5^2*r5*r9, r13 = -6 + d, r14 = -(m4^2*r13) + m5^2*r5, r15 = -3*m3^2 - m4^2*r10 + m5^2*r5, r16 = m3^2*r14 + m2^2*r15 + m2^4*r4 - 2*m3^4*r5 - 3*m4^2*m5^2*r5 + m5^4*r5 + m4^4*r8, r17 = m3^2 + 2*m4^2, r18 = -1 + d, r19 = -(m3^2*r13) - 2*m4^2*r18 + 2*m5^2*r5, r20 = 2*m2^4 - 3*m3^4 + d*m3^4 - 3*m3^2*m4^2 + 2*m4^4 + m2^2*r19 - 2*m5^4*r5 + m5^2*r17*r5, r21 = 2 + d, r22 = 2*m5^2 - m4^2*r21 + m2^2*r4 - m3^2*r4, r23 = -7 + d, r24 = 6*m4^2 - 4*m5^2, r25 = 3*m3^2 + m4^2*r18 + m5^2*r23, r26 = -6*m4^4 - 2*m4^2*m5^2*r23 + m3^2*r24 + 2*m2^2*r25 - 2*m2^4*r4 - m3^4*r4, r27 = m3^4 + m3^2*m4^2 - 2*m4^4, r28 = m3^2 + m4^2*r23, r29 = -2*m4^2*r18 + m3^2*r21 + 2*m5^2*r23, r30 = -6*m2^4 + 2*m5^2*r28 - m2^2*r29 + r27*r4, r31 = m1^4*r22 + m1^2*r26 + m3^2*r30 + m1^6*r4, r32 = m3 - m4, r33 = m3 + m4, r34 = 2*m3^2 + m4^2, r35 = -17 + 3*d, r36 = m3^2*r23 + m4^2*r35, r37 = -9 + d, r38 = 17 - 3*d, r39 = 5*m3^2 + m4^2*r37 + m5^2*r38, r40 = 1 + d, r41 = 5*m4^2 - m5^2*r23 + m2^2*r4 - m3^2*r40, r42 = m5^4*r35 - m5^2*r36 + m2^2*r39 - 2*m1^4*r4 + m2^4*r4 - r32*r33*r34*r4 + m1^2*r41, r43 = m1^2 - m2^2 + m3^2 - m4^2, r44 = 2*m5^2*r13 + r4*r43, r45 = m3^4*r12 + m1^4*r16 + m1^2*m3^2*r20 + PP*r31 + PP^2*r42 + PP^3*r44 + m1^6*r7, r46 = m2^2 + m4^2, r47 = 13 - 3*d, r48 = m4^2*r47 - m5^2*r5 + m3^2*r6, r49 = m5^4*r5 + m5^2*r32*r33*r5 + m4^2*r4*r9, r50 = -18 + 4*d, r51 = -(m4^2*r13) - 3*m5^2*r5, r52 = 2*m3^4*r5 + m4^2*m5^2*r5 + m5^4*r5 + m4^4*r50 + m3^2*r51, r53 = -3*m4^2 + 2*m5^2*r5, r54 = m4^4*r47 + 2*m3^4*r5 + m4^2*m5^2*r5 - 2*m5^4*r5 + m3^2*r53, r55 = m4^2*r13 + 6*m3^2*r5 - 2*m5^2*r5, r56 = 3*m4^2 + m3^2*r5 - m5^2*r5, r57 = 7 - 2*d, r58 = m3^2*r5 + 3*m5^2*r5 + m4^2*r57, r59 = m2^6*r4 + m2^2*m4^2*r55 + m2^4*r56 + m4^4*r58, r60 = m4^2 - m3^2*r5, r61 = 10 - 3*d, r62 = 2*m5^2 + 3*m4^2*r4 + m3^2*r61, r63 = m4^2 + m5^2*r5, r64 = -4*m4^2*m5^2 + 3*m4^4*r4 - 2*m3^4*r5 + 2*m3^2*r63, r65 = m4^2 + m3^2*r5 - m5^2*r5, r66 = 2*m3^2*r5 + 2*m5^2*r5 + m4^2*r61, r67 = 3*m2^4*r4 + 2*m2^2*r65 + m4^2*r66, r68 = -3*m2^6*r4 - 2*m1^4*m4^2*r5 + 2*m4^2*m5^2*r60 + m2^4*r62 + m2^2*r64 + m1^2*r67 - 3*m4^4*r4*r9, r69 = -13 + 3*d, r70 = m3^2*r5 + m4^2*r69, r71 = m4^2 - 3*m2^2*r4 - m3^2*r5 + m5^2*r5, r72 = -5 + d, r73 = m3^2 + m5^2*r69 + m4^2*r72, r74 = 3*m2^4*r4 - m5^4*r5 + m5^2*r70 + m1^2*r71 + m2^2*r73 + 3*m4^2*r4*r9, r75 = m1^2 - m2^2 + m3^2 - m4^2 - 2*m5^2, r76 = m2^8*r4 + m2^6*r48 + m4^4*r49 + 2*m1^4*m4^2*r46*r5 + m2^4*r52 + m2^2*m4^2*r54 - m1^2*r59 + PP*r68 + PP^2*r74 + PP^3*r4*r75, r77 = m3^2 - m4^2 + m5^2, r78 = -2*m2^2 + m4^2 + m5^2, r79 = -2*m1^2 - m3^2 - m4^2 + m5^2, r80 = m1^4 + PP^2 - m1^2*r77 + m3^2*r78 + PP*r79, r81 = m3^2 + m4^2, r82 = m3^2 + m4^2 + m5^2, r83 = m1^2 + m3^2 - m5^2, r84 = m1^4 + 2*m3^2*m4^2 - m4^4 + PP^2 - m2^2*r77 + m5^2*r81 - m1^2*r82 - 2*PP*r83, r85 = m1 - m3, r86 = -PP + r85^2, r87 = m1 + m3, r88 = -PP + r87^2, r89 = m2 - m4, r90 = m2 + m4, r91 = -m1^2 - m2^2 - m3^2 - m4^2 + 2*m5^2, r92 = PP^2 + r85*r87*r89*r90 + PP*r91, r93 = m2^2 - 3*m4^2, r94 = m4 - m5, r95 = m4 + m5, r96 = 2*m3^2 - m4^2 + m5^2, r97 = -m1^2 - m2^2 - 2*m3^2 + 3*m5^2, r98 = PP^2 + m1^2*r93 + m2^2*r94*r95 + m4^2*r96 + PP*r97, r99 = -2 + d, r100 = -m1^2 + m2^2, r101 = m2^2 + m1^2*r72, r102 = m3^2*r101 - 2*m3^4*r4 + m2^2*r100*r4, r103 = 9 - 2*d, r104 = m2^2*r23 + m3^2*r72, r105 = 2*m1^4 + m2^4*r103 + m1^2*r104 + m2^2*m3^2*r5, r106 = -9 + 2*d, r107 = m1 - m2, r108 = m1 + m2, r109 = -(r106*r107*r108) + m3^2*r4, r110 = m2^2*r102 + m4^2*r105 + m4^4*r109 - m4^6*r4, r111 = m1^2 + m2^2, r112 = m2^2*r4 - 2*m1^2*r72, r113 = -19 + 5*d, r114 = m3^2*r112 + m3^4*r113 + m2^2*r111*r4, r115 = m3^2*r5 + m2^2*r6, r116 = 2*m1^4 + 2*m1^2*r115 + m2^4*r13 + m3^4*r72 - 2*m2^2*m3^2*r99, r117 = m2^2*r106 + m3^2*r4 - m1^2*r99, r118 = m2^2*r114 - m4^2*r116 + m4^4*r117 - m4^6*r6, r119 = -(m2^2*r5) + 2*m3^2*r57 + m1^2*r72, r120 = m1^2*r18 + 2*m3^2*r4 - m2^2*r5, r121 = m2^2*r119 + m4^2*r120 + 2*m4^4*r5, r122 = m3^2*r5 + m4^2*r72, r123 = -2*m2^2*r4 - m4^2*r69 + m3^2*r72, r124 = m2^2*r122 + m1^2*r123 + 2*m2^4*r4 + 2*m4^2*r32*r33*r4, r125 = -3*m4^2 + m2^2*r4 - m3^2*r72, r126 = m3^2 - m4^2*r72, r127 = -2*m3^2*m4^2 - 2*m1^2*r125 - 2*m2^2*r126 + m4^4*r18 - 4*m2^4*r4 + m3^4*r72, r128 = -(m2^2*r18) + 2*m4^2*r5 + m1^2*r72 + 2*m3^2*r72, r129 = m5^2*r127 - m5^4*r128 - r124*r32*r33 + m5^6*r72, r130 = -m1^2 + m2^2 + m3^2 - m4^2, r131 = -14 + 3*d, r132 = -(m3^2*r13) + m4^2*r131 + m1^2*r4 + 5*m2^2*r4, r133 = -2*m5^4 + m5^2*r132 + r130*r32*r33*r4, r134 = m5^2*r118 + m5^4*r121 + PP*r129 + PP^2*r133 + r110*r32*r33 - 2*m5^2*PP^3*r4 + m5^6*r5*r89*r90, r135 = m3 - m4 - m5, r136 = m3 + m4 - m5, r137 = m3 - m4 + m5, r138 = m3 + m4 + m5, r139 = -10 + d, r140 = 13 - 2*d, r141 = d*m4^2 + 2*m3^2*r5, r142 = -8 + d, r143 = m4^2*r142 - m3^2*r99 + m5^2*r99, r144 = m3^2*m4^2*r139 + m4^4*r140 - m5^2*r141 + m2^2*r143 + m3^4*r5 + m5^4*r5, r145 = 3*m3^4 - 12*m3^2*m4^2 + 7*m4^4, r146 = 3*m3^2 + 4*m4^2, r147 = m3^2 - 11*m4^2, r148 = 7*m3^4 + 10*m3^2*m4^2 - 17*m4^4 - 5*m5^4 - 2*m5^2*r147, r149 = m2^2 + 2*m3^2 + m4^2, r150 = -m2^4 + m2^2*m3^2 + m3^4 + 3*m2^2*m4^2 + m3^2*m4^2 - m4^4 + m5^4 - m5^2*r149, r151 = 3*m3^6 + 6*m3^4*m4^2 - 17*m3^2*m4^4 + 8*m4^6 + 3*m5^6 - m5^2*r145 - m5^4*r146 + m2^2*r148 - d*r150*r77 + 6*m2^4*r94*r95, r152 = -(m3^2*m4) + m4^3, r153 = 11 - 2*d, r154 = -(d*m3^2*m4^2) + m4^4*r153 + m3^4*r5, r155 = m4^2 + m3^2*r5, r156 = r142*r32*r33 + m5^2*r99, r157 = 11 - 3*d, r158 = -8 + 3*d, r159 = m5^2*r158 + m4^2*r21, r160 = -3*m3^4 + 2*m4^2*m5^2*r106 + m5^4*r157 + m3^2*r159 - m4^4*r18, r161 = -2*m2^6 + m5^2*r154 - 2*m5^4*r155 + m2^4*r156 + m2^2*r160 + r152^2*r4 + m5^6*r5, r162 = m4^2*r23 - 3*m3^2*r72, r163 = -4*m2^2 + m4^2*r18 + m3^2*r23, r164 = -m3^4 + m4^4, r165 = -(m2^4*r13) + m2^2*r162 + m1^2*r163 + r164*r4 + m1^4*r99, r166 = -19 + 4*d, r167 = m4^2 + m3^2*r72, r168 = m3^2 + m4^2*r69, r169 = -2*r168 + 4*m2^2*r4, r170 = -m3^4 + m2^4*r13 - m4^4*r166 + 2*m2^2*r167 + m1^2*r169 + 2*m3^2*m4^2*r72 + m1^4*r99, r171 = m1^2 - m2^2 + 4*m4^2, r172 = -(m5^2*r170) + r165*r32*r33 + m5^6*r72 - m5^4*r171*r72, r173 = m2^2 + m3^2, r174 = -(m4^2*r13) + r131*r173 + m1^2*r8, r175 = m5^2*r174 - 2*m5^4*r4 + r130*r32*r33*r4, r176 = 2*m1^6*m4^2 + m1^4*r144 + m1^2*r151 + m3^2*r161 + PP*r172 + PP^2*r175 - 2*m5^2*PP^3*r4, r177 = m3^2 + m4^2 - m5^2, r178 = -2*m1^2 + m3^2 - m4^2 + m5^2, r179 = -m3^2 + m4^2 + m5^2, r180 = m2^2*r177 + m4^2*r178 + PP*r179, r181 = -2*m2^2 - m3^2 + m4^2 + m5^2, r182 = m1^2*r177 + m3^2*r181 + PP*r77, r183 = -(m2^2*r13) - 2*m3^2*r5, r184 = m1^2*r183 - 2*m3^4*r4 + m2^4*r57 + m1^4*r72 - m2^2*m3^2*r99, r185 = 3*m2^2*r4 + m3^2*r72, r186 = m2^4*r106 + 2*m1^2*r185 + m1^4*r40 - 2*m2^2*m3^2*r6, r187 = r111*r13 - m3^2*r4, r188 = m2^2*r184 + m4^2*r186 - m4^4*r187 + m4^6*r4, r189 = 2*m1^2 + m3^2*r10 + 2*m2^2*r5, r190 = m2^2*r5 + m3^2*r72 + 2*m1^2*r99, r191 = m2^2*r189 - m4^2*r190 - m4^4*r5, r192 = -(m3^2*r5) - m4^2*r72, r193 = 2*m2^2*r4 + m4^2*r69 - m3^2*r72, r194 = m2^2*r192 + m1^2*r193 - 2*m2^4*r4 + 2*m4^2*r4*r9, r195 = m2^2 + m4^2 + m3^2*r72, r196 = -(m3^2*r6) - m4^2*r72, r197 = m2^4*r157 + 2*m1^2*r195 + 2*m2^2*r196 + 2*m4^2*r17*r4 + m1^4*r72, r198 = m4^2*r10 - 2*m2^2*r5 + 2*m1^2*r72 + m3^2*r72, r199 = r107*r108*r194 + m5^2*r197 - m5^4*r198 + m5^6*r72, r200 = m1^2 - m2^2 - m3^2 + m4^2, r201 = m1^2 + m2^2 + m3^2 + 5*m4^2, r202 = 2*m5^4 - r107*r108*r200 - m5^2*r201, r203 = r107*r108*r110 - m5^2*r188 - m5^4*r191 + PP*r199 + 2*m5^2*PP^3*r4 + PP^2*r202*r4 + m5^6*r5*r89*r90, r204 = m4^2 + m5^2, r205 = -2*m5^2*r5 + m4^2*r99, r206 = 18 - 5*d, r207 = m4^2*r206 + m5^2*r8 - 2*m3^2*r99, r208 = m2^2*r207 + 2*m2^4*r4 - m3^4*r5 - m3^2*r204*r5 + r205*r94*r95, r209 = 2*m3^2*m4^2 + m4^4*r142 + 2*m3^4*r5, r210 = -(m4^2*r18) + m3^2*r5, r211 = 3 - 2*d, r212 = m5^2 + m4^2*r157 + m3^2*r211, r213 = m4^2*r106 + m3^2*r4, r214 = -(d*m3^4) + 10*m3^2*m4^2 - 2*d*m3^2*m4^2 - 2*m4^4 + d*m4^4 + 2*m5^2*r213 - 2*m5^4*r4, r215 = d*m3^2*m4^4 - 2*m4^6 - m5^2*r209 + m5^4*r210 + m2^4*r212 + m2^2*r214 + m2^6*r4 + m5^6*r5 - m3^4*m4^2*r99, r216 = m4^2*r13 + m3^2*r99, r217 = m3^2*r5 - m4^2*r72, r218 = 13 - 4*d, r219 = 3*m3^2 + m5^2*r218 + m4^2*r23, r220 = m4^2*r142 + m5^2*r61, r221 = 2*m3^4 + 2*m4^2*m5^2 - m4^4*r13 + m3^2*r220 + 2*m5^4*r6, r222 = m4^2*m5^2*r216 + m5^4*r217 + m2^4*r219 + m2^2*r221 - m5^6*r5 + m2^6*r99, r223 = -(m3^2*r10) + m4^2*r5, r224 = 4*m3^2*m4^2 + m1^2*r122 + m4^4*r13 + m2^2*r223 + m1^4*r4 - m2^4*r4 - m3^4*r99, r225 = -m3^2 + m2^2*r72 - m4^2*r72, r226 = -2*m4^2*r106 + 2*m3^2*r69, r227 = m1^4*r106 + m2^4*r106 - m4^4*r13 - 2*m1^2*r225 + m2^2*r226 - 4*m3^2*m4^2*r4 - m3^4*r99, r228 = m3^2 + 3*m4^2, r229 = r107*r108*r224 - m5^2*r227 + m5^6*r72 - m5^4*r228*r72, r230 = m4^2*r131 + m1^2*r4 + m2^2*r4 + m3^2*r8, r231 = 2*m5^4*r106 - m5^2*r230 - r107*r108*r200*r4, r232 = m1^4*r208 - m1^2*r215 - m3^2*r222 + PP*r229 + PP^2*r231 + 2*m5^2*PP^3*r4 + m1^6*r7, r233 = -2*m3^2 + m4^2, r234 = -m2^2 + m4^2 - 2*m5^2, r235 = -m1^2 + m2^2 + m5^2, r236 = m1^4 + m5^4 + m2^2*r233 + m1^2*r234 + PP*r235 - m5^2*r46, r237 = -m2^2 + m5^2, r238 = m2^2 + m3^2 - 2*m4^2 + m5^2, r239 = -m1^2 + m2^2 - m5^2, r240 = m1^4 + m3^2*r237 - m1^2*r238 + PP*r239, r241 = m3^2 + 3*m4^2 - m5^2, r242 = -3*m3^2 - m4^2 + m5^2, r243 = m5^4 - m5^2*r228 + m1^2*r241 + m2^2*r242 + 2*PP*r32*r33 + 2*m4^2*r9, r244 = 2*m1^2 + m2^2 + m4^2, r245 = -2*m1^2 - m3^2 - m4^2 + 3*m5^2, r246 = m1^4 - 3*m2^2*m3^2 + m5^4 + PP^2 + m4^2*r173 - m5^2*r244 + PP*r245, r247 = -2*m3^2 + m4^2 + m5^2, r248 = -m2^4 - m4^2*m5^2 + PP*r235 + m2^2*r247 + m1^2*r46, r249 = m2^2*r153 + m1^2*r5, r250 = 2*m1^2 + m2^2*r4, r251 = m2^2*r13 + m1^2*r139, r252 = r107*r108*r250 + m3^2*r251 - m3^4*r4, r253 = m1^2*r140 + 2*m3^2*r4 + m2^2*r72, r254 = m3^4*r249 + m4^2*r252 + m4^4*r253 - m4^6*r4 + m2^2*m3^2*r100*r99, r255 = 2*m3^2 + m4^2*r13, r256 = -2*m3^2*r5 + m2^2*r99 - m4^2*r99, r257 = -11 + 2*d, r258 = -(m4^4*r106) + 2*m3^2*m4^2*r23 - m3^4*r257, r259 = 4*m4^2 + m3^2*r13, r260 = -2*m2^4 + 6*m3^2*m4^2 + 2*m2^2*r259 + m4^4*r37 + m3^4*r5, r261 = -5*m3^4*m4^2 + m2^4*r255 + m1^4*r256 + m2^2*r258 + m1^2*r260 - m2^6*r4 + m3^6*r5 + m4^6*r6 - 3*m3^2*m4^4*r72, r262 = m3^4 + m3^2*m4^2 + m4^4, r263 = m1^4 + m2^4 - 2*r262 + m1^2*r81 + m2^2*r81, r264 = m1^2 + m2^2 - m3^2 - m4^2, r265 = -(r13*r32*r33) + m2^2*r99, r266 = -2*m1^2*r265 - r32^2*r33^2*r4 + 2*m2^2*r13*r9 + m1^4*r99 + m2^4*r99, r267 = m3^2*r13 + m4^2*r4, r268 = -16 + 3*d, r269 = m3^2*r13 - m4^2*r268 + m2^2*r4, r270 = 2*m2^2*r267 + 2*m1^2*r269 + r13*r228*r32*r33 + m2^4*r61 + m1^4*r99, r271 = 2*m2^2 + m4^2*r23 - m3^2*r72, r272 = -(m5^2*r270) - 2*m5^4*r271 + r266*r32*r33, r273 = 2*m3^2 - 2*m4^2 - m5^2, r274 = m1^2*r5 - m2^2*r5 + r273*r72, r275 = r200*r254 + m5^2*r261 + PP*r272 + 2*m5^2*PP^2*r274 + m5^4*r263*r5 - m5^6*r264*r5, r276 = -2*m2^2*m3^2 - 2*m3^4 + 3*m3^2*m4^2 - m4^4 + 3*m3^2*m5^2 + 2*m4^2*m5^2 - m5^4 + m1^2*r177 + PP*r77, r277 = -(m4^2*r106) + m2^2*r4 - m3^2*r5, r278 = -2*m3^4 - m3^2*m4^2*r13 + m2^2*r196 + m2^4*r4 + m4^4*r4, r279 = m4^2*r131 + m3^2*r8, r280 = m2^2*r279 - 2*m2^4*r4 + m4^2*r32*r33*r99, r281 = m1^4*r277 + m2^2*r278 + m1^2*r280, r282 = 11*m3^2 - 3*d*m3^2 + 9*m4^2 - 2*d*m4^2, r283 = 15 - 4*d, r284 = m4^2*r106 + m2^2*r283 + m3^2*r5, r285 = m4^4*r13 + 4*m3^2*m4^2*r5 - m3^4*r99, r286 = -m4^2 + m3^2*r5, r287 = -(m4^2*r5) + m3^2*r6, r288 = 2*m2^2*r287 + m2^4*r72 - 2*r286*r81, r289 = -2*m3^2*m4^4 + m2^4*r282 + m1^4*r284 + m2^2*r285 + m1^2*r288 - m4^6*r4 + m1^6*r5 + m2^6*r6 + m3^4*m4^2*r99, r290 = 2*m2^2 - m3^2 - m4^2, r291 = 2*m1^4 + 2*m2^4 - m3^4 - m4^4 + m1^2*r290 - m2^2*r81, r292 = m2^2 - m3^2 + m4^2, r293 = m1^4*r4 + m2^4*r4 - 2*m1^2*r292*r4 + 2*m2^2*r4*r9 - r32^2*r33^2*r99, r294 = m3^2*r13 - m4^2*r131, r295 = m2^2*r13 - r4*r81, r296 = m1^4*r131 + 2*m2^2*r294 - 2*m1^2*r295 - 2*m3^2*m4^2*r4 + m4^4*r8 - m2^4*r99 - m3^4*r99, r297 = 2*m4^2 - m2^2*r5 + m1^2*r72, r298 = r107*r108*r293 - m5^2*r296 + 2*m5^4*r297, r299 = -2*m5^2*r32*r33*r5 + 2*m5^4*r72, r300 = r130*r281 - m5^2*r289 + PP*r298 + PP^2*r299 - m5^6*r264*r5 + m5^4*r291*r5, r301 = -2*m2^2*m3^2 - m3^2*m4^2 + m4^4 + m5^4 - m5^2*r17 + m1^2*r177 + PP*r77, r302 = m2^2 + 2*m3^2 - 3*m4^2, r303 = -m1^2 + m2^2 - 3*m5^2, r304 = m1^4 - m2^2*m4^2 - m5^4 + m5^2*r149 - m1^2*r302 + PP*r303, r305 = -((r45*TBI[d, PP, {{1, m4}, {1, m2}}]* TBI[d, PP, {{2, m1}, {1, m3}}])/(4*r3)) + (r76*TBI[d, PP, {{1, m3}, {1, m1}}]* TBI[d, PP, {{2, m2}, {1, m4}}])/(4*r3) - (r80*TBI[d, PP, {{2, m1}, {1, m3}}]* TBI[d, PP, {{2, m2}, {1, m4}}])/2 - (r45*TBI[d, PP, {{1, m4}, {1, m2}}]* TBI[d, PP, {{2, m3}, {1, m1}}])/(4*r3) - (r84*TBI[d, PP, {{2, m2}, {1, m4}}]* TBI[d, PP, {{2, m3}, {1, m1}}])/2 - r86*r88*TBI[d, PP, {{1, m4}, {1, m2}}]* TBI[d, PP, {{2, m3}, {2, m1}}] + (r76*TBI[d, PP, {{1, m3}, {1, m1}}]* TBI[d, PP, {{2, m4}, {1, m2}}])/(4*r3) - (r92*TBI[d, PP, {{2, m1}, {1, m3}}]* TBI[d, PP, {{2, m4}, {1, m2}}])/2 - (r98*TBI[d, PP, {{2, m3}, {1, m1}}]* TBI[d, PP, {{2, m4}, {1, m2}}])/2 - r86*r88*TBI[d, PP, {{1, m4}, {1, m2}}]* TBI[d, PP, {{3, m1}, {1, m3}}] - r86*r88*TBI[d, PP, {{1, m4}, {1, m2}}]* TBI[d, PP, {{3, m3}, {1, m1}}] - r3*TFI[r99, PP, {{1, m1}, {1, m2}, {1, m3}, {1, m4}, {1, m5}}] - (r134*TVI[d, PP, {{1, m5}, {1, m1}, {2, m4}, {1, m3}}])/ (4*r3) - (r135*r136*r137*r138* TVI[d, PP, {{1, m5}, {1, m1}, {2, m4}, {2, m3}}])/2 - (r176*TVI[d, PP, {{1, m5}, {1, m2}, {2, m3}, {1, m4}}])/(4*r3) + (r180*TVI[d, PP, {{1, m5}, {1, m2}, {2, m3}, {2, m4}}])/2 - r182*TVI[d, PP, {{1, m5}, {1, m2}, {3, m3}, {1, m4}}] + (r203*TVI[d, PP, {{1, m5}, {1, m3}, {2, m2}, {1, m1}}])/ (4*r3) + (r232* TVI[d, PP, {{1, m5}, {1, m4}, {2, m1}, {1, m2}}])/ (4*r3) + (r236* TVI[d, PP, {{1, m5}, {1, m4}, {2, m1}, {2, m2}}])/2 + r240*TVI[d, PP, {{1, m5}, {1, m4}, {3, m1}, {1, m2}}] + (r45*TVI[d, PP, {{1, m5}, {2, m1}, {1, m4}, {1, m3}}])/ (4*r3) + (r86*r88* TVI[d, PP, {{1, m5}, {2, m1}, {1, m4}, {2, m3}}])/2 + (r92*TVI[d, PP, {{1, m5}, {2, m1}, {2, m4}, {1, m3}}])/2 - (r76*TVI[d, PP, {{1, m5}, {2, m2}, {1, m3}, {1, m4}}])/ (4*r3) - (r243* TVI[d, PP, {{1, m5}, {2, m2}, {2, m3}, {1, m4}}])/2 + (r45*TVI[d, PP, {{1, m5}, {2, m3}, {1, m2}, {1, m1}}])/(4*r3) + (r86*r88*TVI[d, PP, {{1, m5}, {2, m3}, {1, m2}, {2, m1}}])/2 + (r246*TVI[d, PP, {{1, m5}, {2, m3}, {2, m2}, {1, m1}}])/2 - (r76*TVI[d, PP, {{1, m5}, {2, m4}, {1, m1}, {1, m2}}])/ (4*r3) + (r248* TVI[d, PP, {{1, m5}, {2, m4}, {2, m1}, {1, m2}}])/2 + r86*r88*TVI[d, PP, {{1, m5}, {3, m1}, {1, m4}, {1, m3}}] + r86*r88*TVI[d, PP, {{1, m5}, {3, m3}, {1, m2}, {1, m1}}] + (r275*TVI[d, PP, {{2, m5}, {1, m1}, {1, m4}, {1, m3}}])/ (4*r3) + (r276* TVI[d, PP, {{2, m5}, {1, m1}, {1, m4}, {2, m3}}])/2 - (r180*TVI[d, PP, {{2, m5}, {1, m1}, {2, m4}, {1, m3}}])/2 - (r275*TVI[d, PP, {{2, m5}, {1, m2}, {1, m3}, {1, m4}}])/ (4*r3) + (r180* TVI[d, PP, {{2, m5}, {1, m2}, {1, m3}, {2, m4}}])/2 - (r276*TVI[d, PP, {{2, m5}, {1, m2}, {2, m3}, {1, m4}}])/2 - (r300*TVI[d, PP, {{2, m5}, {1, m3}, {1, m2}, {1, m1}}])/ (4*r3) - (r240* TVI[d, PP, {{2, m5}, {1, m3}, {1, m2}, {2, m1}}])/2 - (r236*TVI[d, PP, {{2, m5}, {1, m3}, {2, m2}, {1, m1}}])/2 + (r300*TVI[d, PP, {{2, m5}, {1, m4}, {1, m1}, {1, m2}}])/ (4*r3) + (r236* TVI[d, PP, {{2, m5}, {1, m4}, {1, m1}, {2, m2}}])/2 + (r240*TVI[d, PP, {{2, m5}, {1, m4}, {2, m1}, {1, m2}}])/2 + (r182*TVI[d, PP, {{2, m5}, {2, m1}, {1, m4}, {1, m3}}])/2 - (r301*TVI[d, PP, {{2, m5}, {2, m2}, {1, m3}, {1, m4}}])/2 - (r304*TVI[d, PP, {{2, m5}, {2, m3}, {1, m2}, {1, m1}}])/2 + (r248*TVI[d, PP, {{2, m5}, {2, m4}, {1, m1}, {1, m2}}])/2, r306}, r306 = Factor /@ r305/(PP*r1*r2); r306]) /; n1 === 1 && n2 === 1 && n3 === 1 && n4 === 1 && n5 === 1 && MatchQ[d, _Symbol + _Integer?Positive] && PP =!= 0 && Cayley[m1, m2, m3, m4, m5, Sqrt[PP]] =!= 0]; \ \>", "Input", Editable->False] }, Closed]], Cell[CellGroupData[{ Cell["Input (51)", "Subsection", CellTags->"T1.6.16.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_51\), "=", RowBox[{ RowBox[{\(\[CapitalDelta]\_\(1, 3, 4\)\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}], "==", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"2", \(m\_3\%2\), \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True]}], ")"}]}], "+", RowBox[{\(u\_\(4, 1, 3\)\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True]}], ")"}]}], "+", \(\(u\_\(1, 3, 4\)\) \((d - \[Nu]\_1 - 2 \[Nu]\_3)\)\), "+", \(2 \( m\_3\%2\) \((\[Nu]\_1 - \[Nu]\_3)\)\)}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_51 = OperatorApplyV[e\_51]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (51)", "Subsection", CellTags->"T1.6.17.1"], Cell[BoxData[ \(s\_51\)], "Input"], Cell[BoxData[ \(h\_51 = s\_51 /. \[Nu]\_1 \[Rule] \[Nu]\_1 - 1\)], "Input"], Cell[BoxData[ RowBox[{\(f\_51\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_51\), ",", "\"\<(51)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", \(\[Nu]\_1 > 1 && \[CapitalDelta]\_\(1, 3, 4\) =!= 0\), "]"}]}], "]"}]}]], "Input"], Cell[BoxData[ \(CheckTVIRecursion[f\_51]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (52)", "Subsection", CellTags->"T1.6.18.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_52\), "=", RowBox[{ RowBox[{\(\[CapitalDelta]\_\(2, 4, 6\)\), \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}], "==", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"2", \(m\_1\%2\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}], ")"}]}], "+", RowBox[{"2", \(m\_3\%2\), \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}], ")"}]}], "-", RowBox[{"2", \(m\_4\%2\), \(\[Nu]\_4\), InterpretationBox[ StyleBox[\(4\^+\), FontWeight->"Bold"], Schiebe[ 4, "+"], Editable->True], InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}], "+", RowBox[{\((2 m\_2\%2 - u\_\(4, 2, 6\))\), \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True]}], "-", RowBox[{\((\[CapitalSigma]\_4 + 2)\), RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}], ")"}]}], "+", \(\(u\_\(2, 4, 6\)\) \((d - 3 \[Nu]\_2)\)\), "+", \(2 \( m\_4\%2\) \((\[Nu]\_4 - \[Nu]\_2)\)\)}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_52 = OperatorApplyV[e\_52]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (52)", "Subsection", CellTags->"T1.6.19.1"], Cell[BoxData[ \(h\_52 = \[Nu]explicit[s\_52] /. \[Nu]\_2 \[Rule] \[Nu]\_2 - 1\)], "Input"], Cell[BoxData[ RowBox[{\(f\_52\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_52\), ",", "\"\<(52)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", \(\[Nu]\_2 > 1 && \[CapitalDelta]\_\(2, 4, 6\) =!= 0\), "]"}]}], "]"}]}]], "Input"], Cell[BoxData[ \(CheckTVIRecursion[f\_52]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (53)", "Subsection", CellTags->"T1.6.20.1"], Cell[BoxData[ \(h\_53 = Interchange[s\_51, 1 \[LeftRightArrow] 3] /. \[Nu]\_3 \[Rule] \[Nu]\_3 - 1\)], "Input"], Cell[BoxData[ RowBox[{\(f\_53\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_53\), ",", "\"\<(53)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", \(\[Nu]\_3 > 1 && \[CapitalDelta]\_\(3, 1, 4\) =!= 0\), "]"}]}], "]"}]}]], "Input"], Cell[BoxData[ \(CheckTVIRecursion[f\_53]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (54)", "Subsection", CellTags->"T1.6.21.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_54\), "=", RowBox[{ RowBox[{"2", \(m\_3\%2\), \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}], "==", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{\(u\_\(4, 1, 3\)\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True]}], "+", RowBox[{\(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}], ")"}]}], "+", "\n", "\t\t\t\t", \((d - \[Nu]\_1 - 2 \[Nu]\_3)\)}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_54 = OperatorApplyV[e\_54]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (54)", "Subsection", CellTags->"T1.6.22.1"], Cell[BoxData[ \(h\_54 = s\_54 /. \[Nu]\_3 \[Rule] \[Nu]\_3 - 1\)], "Input"], Cell[BoxData[ RowBox[{\(f\_54\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_54\), ",", "\"\<(54)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", " ", \(\[Nu]\_3 > 1 && \ m3 =!= 0\), "]"}]}], "]"}]}]], "Input"], Cell[BoxData[ \(CheckTVIRecursion[f\_54]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (55)", "Subsection", CellTags->"T1.6.23.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_55\), "=", RowBox[{ RowBox[{"2", " ", \(m\_4\%2\), \(\[Nu]\_4\), InterpretationBox[ StyleBox[\(4\^+\), FontWeight->"Bold"], Schiebe[ 4, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}], "==", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{\(u\_\(3, 1, 4\)\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True]}], "+", RowBox[{\(u\_\(6, 2, 4\)\), \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True]}], "+", "\n", "\t\t\t\t", RowBox[{\(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True]}], ")"}]}], "-", RowBox[{\(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True]}], "+", \((d - \[Nu]\_1 - \[Nu]\_2 - 2 \[Nu]\_4)\)}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_55 = OperatorApplyV[e\_55]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (55)", "Subsection", CellTags->"T1.6.24.1"], Cell[BoxData[ \(h\_55 = s\_55 /. \[Nu]\_4 \[Rule] \[Nu]\_4 - 1\)], "Input"], Cell[BoxData[ RowBox[{\(f\_55\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_55\), ",", "\"\<(55)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", \(\[Nu]\_4 > 1 && \ m4 =!= 0\ && \ \[Nu]\_3 > 1\), "]"}]}], "]"}]}]], "Input"], Cell[BoxData[ \(CheckTVIRecursion[f\_55]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (56)", "Subsection", CellTags->"T1.6.25.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_56\), "=", RowBox[{ RowBox[{"2", " ", \(m\_4\%2\), \(\[Nu]\_4\), InterpretationBox[ StyleBox[\(4\^+\), FontWeight->"Bold"], Schiebe[ 4, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}], "==", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{\(-2\), \(m\_1\%2\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True]}], "+", RowBox[{\(u\_\(6, 2, 4\)\), \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True]}], "-", RowBox[{"2", \(m\_3\%2\), \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True]}], "-", "\n", "\t\t\t\t", RowBox[{\(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True]}], "+", \((2 d - 2 \[Nu]\_1 - \[Nu]\_2 - 2 \[Nu]\_3 - 2 \[Nu]\_4) \)}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_56 = OperatorApplyV[e\_56]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (56)", "Subsection", CellTags->"T1.6.26.1"], Cell[BoxData[ \(h\_56 = s\_56 /. \[Nu]\_4 \[Rule] \[Nu]\_4 - 1\)], "Input"], Cell[BoxData[ RowBox[{\(f\_56\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_56\), ",", "\"\<(56)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", \(\[Nu]\_4 > 1 && \ m4 =!= 0\ && \ \[Nu]\_3 === 1\), "]"}]}], "]"}]}]], "Input"], Cell[BoxData[ \(CheckTVIRecursion[f\_56]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (59)", "Subsection", CellTags->"T1.6.27.1"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\[CapitalDelta]\_\(1, 3, 4\)\)]], "== 0 but all ", Cell[BoxData[ \(m\_i\%2\)]], " != 0" }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_59\), "=", RowBox[{ RowBox[{ \((2 \( m\_1\%2\) \(u\_\(1, 3, 4\)\) \((d - \[Nu]\_1 - 2 \[Nu]\_3)\) + \((\[Nu]\_3 - 1)\) u\_\(4, 1, 3\)\%2 + \n\t 4 \( m\_1\%2\) \(m\_3\%2\) \((\[Nu]\_1 - \[Nu]\_3)\))\), InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}], "==", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{\(u\_\(4, 1, 3\)\), \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True], InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True]}], ")"}]}], "-", "\n", "\t", RowBox[{"4", \(m\_1\%2\), \(m\_3\%2\), \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True], InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True]}], "+", RowBox[{ \((4 \( m\_1\%2\) m\_3\%2 + u\_\(4, 1, 3\)\%2)\), \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True], InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True]}], "+", RowBox[{\(u\_\(4, 1, 3\)\), \((\[Nu]\_3 - 1)\), InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True]}], "-", "\n", "\t\t", RowBox[{ \((d - 2 \[Nu]\_1 - \[Nu]\_3 + 1)\), \(u\_\(4, 1, 3\)\), InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}], "+", RowBox[{ \((d - 2 \[Nu]\_1 - 2 \[Nu]\_3 + 1)\), \(u\_\(4, 1, 3\)\), InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True]}]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_59 = OperatorApplyV[e\_59]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (59)", "Subsection", CellTags->"T1.6.28.1"], Cell[BoxData[ \(h\_59 = s\_59\)], "Input"], Cell[BoxData[ RowBox[{\(f\_59\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_59\), ",", "\"\<(59)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", \(\[CapitalDelta]\_\(1, 3, 4\) == 0 && \((4\ m\_3\%2\ m\_1\%2 - 4\ m\_3\%2\ \[Nu]\_3\ m\_1\%2 + 2\ d\ u\_\(1, 3, 4\)\ m\_1\%2 - 4\ \[Nu]\_3\ u\_\(1, 3, 4\)\ m\_1\%2 - 2\ u\_\(1, 3, 4\)\ m\_1\%2 + \[Nu]\_3\ u\_\(4, 1, 3\)\%2 - u\_\(4, 1, 3\)\%2)\)\ \ =!= 0 && n1\ === \ 1 && \ n2\ === \ 1 && \ n4\ === \ 1 && MatchQ[d, _Integer]\), "]"}]}], "]"}]}]], "Input"], Cell["CheckTVIRecursion not applicable .", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Input (60) ", "Subsection", CellTags->"T1.6.29.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_60\), "=", RowBox[{ RowBox[{"2", \(m\_1\%2\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}], "==", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{\(u\_\(4, 1, 3\)\), \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True]}], "+", RowBox[{\(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True]}], ")"}]}], "+", "\n", "\t\t\t\t", \((d - \[Nu]\_3 - 2 \[Nu]\_1)\)}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_60 = OperatorApplyV[e\_60]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (60)", "Subsection", CellTags->"T1.6.30.1"], Cell[BoxData[ \(h\_60 = s\_60 /. \[Nu]\_1 \[Rule] \[Nu]\_1 - 1\)], "Input"], Cell[BoxData[ RowBox[{\(notnecessaryf\_60\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_60\), ",", "\"\<(60)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", \(\[Nu]\_1 > 1 && \ m1 =!= 0\), "]"}]}], "]"}]}]], "Input"], Cell[BoxData[ \(CheckTVIRecursion[notnecessaryf\_60]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (61) ", "Subsection", CellTags->"T1.6.31.1"], Cell[TextData[{ " ( ", Cell[BoxData[ \(m\_1\%2\)]], "== 0 && ", Cell[BoxData[ \(m\_4\%2\)]], "== ", Cell[BoxData[ \(m\_3\%2\)]], " ) \[DoubleLongRightArrow] ( ", Cell[BoxData[ \(TraditionalForm\`\[CapitalDelta]\_\(1, 3, 4\)\)]], "== 0 )" }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_61\), "=", RowBox[{ RowBox[{\((d - 2 \[Nu]\_1 - \[Nu]\_3)\), InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}], "==", RowBox[{\(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_61 = OperatorApplyV[e\_61]\)], "Input"], Cell[TextData[{ "For ( ", Cell[BoxData[ \(m\_3\%2\)]], "== 0 && ", Cell[BoxData[ \(m\_4\%2\)]], "== ", Cell[BoxData[ \(m\_1\%2\)]], " ) \[DoubleLongRightArrow] ( ", Cell[BoxData[ \(TraditionalForm\`\[CapitalDelta]\_\(1, 3, 4\)\)]], "== 0 )\nuse ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"(", RowBox[{ InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True], "==", InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}], ")"}], " "}], TextForm]]], " and switch the masses accordingly." }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (61)", "Subsection", CellTags->"T1.6.32.1"], Cell[TextData[{ "( ", Cell[BoxData[ \(m\_1\%2\)]], "== 0 && ", Cell[BoxData[ \(m\_4\%2\)]], "== ", Cell[BoxData[ \(m\_3\%2\)]], " ) \[DoubleLongRightArrow] ( ", Cell[BoxData[ \(TraditionalForm\`\[CapitalDelta]\_\(1, 3, 4\)\)]], "== 0 )" }], "Text"], Cell[BoxData[ \(h\_61 = s\_61\)], "Input"], Cell[BoxData[ RowBox[{\(f\_61\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_61\), ",", "\"\<(61)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", RowBox[{ RowBox[{ InterpretationBox[\(m\_1\), m1], "===", "0"}], "&&", RowBox[{ InterpretationBox[\(m\_3\), m3], "===", InterpretationBox[\(m\_4\), m4]}]}], "]"}], ",", \({n1 :> 1, n4 :> 1}\)}], "]"}]}]], "Input"], Cell["CheckTVIRecursion not applicable .", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (6153)", "Subsection", CellTags->"T1.6.33.1"], Cell[TextData[{ " ( ", Cell[BoxData[ \(m\_3\%2\)]], "== 0 && ", Cell[BoxData[ \(m\_4\%2\)]], "== ", Cell[BoxData[ \(m\_1\%2\)]], ") \[DoubleLongRightArrow] ( ", Cell[BoxData[ \(TraditionalForm\`\[CapitalDelta]\_\(1, 3, 4\)\)]], "== 0 )" }], "Text"], Cell[BoxData[ \(h\_6153 = Interchange[s\_61, 1 \[LeftRightArrow] 3]\)], "Input"], Cell[BoxData[ RowBox[{\(f\_6153\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_6153\), ",", "\"\<(6153)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", RowBox[{ RowBox[{ InterpretationBox[\(m\_3\), m3], "===", "0"}], "&&", RowBox[{ InterpretationBox[\(m\_1\), m1], "===", InterpretationBox[\(m\_4\), m4]}]}], "]"}], ",", \({n3 :> 1, n4 :> 1}\)}], "]"}]}]], "Input"], Cell["CheckTVIRecursion not applicable .", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Input (62) ", "Subsection", CellTags->"T1.6.34.1"], Cell[TextData[{ "( ", Cell[BoxData[ \(m\_4\%2\)]], "== 0 && ", Cell[BoxData[ \(m\_1\%2\)]], "== ", Cell[BoxData[ \(m\_3\%2\)]], " ) \[DoubleLongRightArrow] (", Cell[BoxData[ \(TraditionalForm\`\(\ \[CapitalDelta]\_\(1, 3, 4\)\)\)]], "== 0 )\nlower ", Cell[BoxData[ \(TraditionalForm\`\[Nu]\_2\)]], " via (52) to one first" }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_62\), "=", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ InterpretationBox[\(p\^2\), PP], "-", \(m\_2\%2\)}], ")"}], \((\[Nu]\_1 - 2 \[Nu]\_2 + 2 \[Nu]\_4 + 2)\), InterpretationBox[ StyleBox[\(4\^+\), FontWeight->"Bold"], Schiebe[ 4, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}], "==", "\n", "\t\t", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{\((m\_1\%2 - u\_\(6, 1, 2\))\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True]}], "+", RowBox[{"4", \(m\_2\%2\), \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True]}], "+", RowBox[{"2", \(m\_1\%2\), \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True]}], "+", "\n", "\t\t\t\t", RowBox[{ RowBox[{"(", RowBox[{\(\[CapitalSigma]\_4\), "-", RowBox[{"2", \(m\_1\%2\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True]}], "-", RowBox[{"2", \(m\_1\%2\), \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True]}]}], ")"}], InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True], InterpretationBox[ StyleBox[\(4\^+\), FontWeight->"Bold"], Schiebe[ 4, "+"], Editable->True]}], "+", RowBox[{ RowBox[{"(", RowBox[{ InterpretationBox[\(p\^2\), PP], "-", \(m\_2\%2\)}], ")"}], \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ StyleBox[\(4\^+\), FontWeight->"Bold"], Schiebe[ 4, "+"], Editable->True], InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}], "-", "\n", "\t\t\t\t", \(\[CapitalSigma]\_4\)}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_62 = OperatorApplyV[e\_62]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (62)", "Subsection", CellTags->"T1.6.35.1"], Cell[BoxData[ \(h\_62 = \[Nu]explicit[s\_62] /. \[Nu]\_4 \[Rule] \[Nu]\_4 - 1\)], "Input"], Cell[BoxData[ RowBox[{\(f\_62\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_62\), ",", "\"\<(62)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", RowBox[{ RowBox[{ InterpretationBox[\(p\^2\), PP], "=!=", InterpretationBox[\(m\_2\%2\), Power[ m2, 2]]}], "&&", \(\[Nu]\_1 - 2\ \[Nu]\_2 + 2\ \[Nu]\_4 =!= 0\)}], "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{ InterpretationBox[\(m\_4\), m4], "\[RuleDelayed]", "0"}], ",", RowBox[{ InterpretationBox[\(m\_3\), m3], "\[RuleDelayed]", InterpretationBox[\(m\_1\), m1]}], ",", \(n2 \[RuleDelayed] 1\)}], "}"}]}], "]"}]}]], "Input"], Cell["CheckTVIRecursion not applicable .", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Input (63) ", "Subsection", CellTags->"T1.6.36.1"], Cell[TextData[{ Cell[BoxData[ \(m\_4\%2\)]], "== 0 && ", Cell[BoxData[ \(TraditionalForm\`\(\ \[CapitalDelta]\_\(1, 3, 4\)\)\)]], " != 0\nreplace (55) by the following" }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_63\), "=", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ InterpretationBox[\(p\^2\), PP], "-", \(m\_2\%2\)}], ")"}], \((\((m\_3\%2 - m\_1\%2)\) \((d - 2 \[Nu]\_2 - 2 \[Nu]\_3 + 2 \[Nu]\_4)\) + 2 \( m\_3\%2\) \((\[Nu]\_3 - \[Nu]\_1)\))\), InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}], "==", "\n", "\t\t", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{\((m\_1\%2 - m\_3\%2)\), RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"2", \(m\_1\%2\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True]}], "+", RowBox[{"2", \(m\_3\%2\), \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True]}], "-", \(\[CapitalSigma]\_4\), "-", "2"}], ")"}], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True]}], ")"}]}], "-", RowBox[{"4", \(m\_2\%2\), \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True]}]}], ")"}]}], "+", "\n", "\t\t\t\t", RowBox[{"2", RowBox[{"(", RowBox[{ InterpretationBox[\(p\^2\), PP], "-", \(m\_2\%2\)}], ")"}], RowBox[{"(", RowBox[{ RowBox[{\(m\_3\%2\), \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True]}], ")"}]}], "+", RowBox[{\(m\_1\%2\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}], ")"}]}]}], ")"}]}]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_63 = OperatorApplyV[e\_63]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (63)", "Subsection", CellTags->"T1.6.37.1"], Cell[TextData[{ Cell[BoxData[ \(m\_4\%2\)]], "== 0 && ", Cell[BoxData[ \(TraditionalForm\`\(\ \[CapitalDelta]\_\(1, 3, 4\)\)\)]], " != 0" }], "Text"], Cell[BoxData[ \(h\_63 = \[Nu]explicit[s\_63]\)], "Input"], Cell[BoxData[ RowBox[{\(f\_63\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_63\), ",", "\"\<(63)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", \(PP\ =!= \ m2^2 && \(Cayley[1, 3, 4]\)[{m1, m2, m3, m4}] =!= 0\), "]"}], ",", RowBox[{"{", RowBox[{ InterpretationBox[\(m\_4\), m4], "\[RuleDelayed]", "0"}], "}"}]}], "]"}]}]], "Input"], Cell[BoxData[ \(CheckTVIRecursion[f\_63]\)], "Input"], Cell[BoxData[ RowBox[{\(f\_63\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_63\), ",", "\"\<(63)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", \(PP\ =!= \ m2^2 && \(Cayley[1, 3, 4]\)[{m1, m2, m3, m4}] =!= 0\), "]"}], ",", RowBox[{"{", RowBox[{ RowBox[{ InterpretationBox[\(m\_4\), m4], "\[RuleDelayed]", "0"}], ",", \(n1 :> 1\), ",", \(n3 :> 1\)}], "}"}]}], "]"}]}]], "Input"], Cell["\<\ CheckTVIRecursion not applicable for special indices since A's and B's appear . \ \>", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (6552)", "Subsection", CellTags->"T1.6.38.1"], Cell[BoxData[ \(r\_6552 = \[Nu]explicit[e\_52] /. \[CapitalDelta]\_\(2, 4, 6\) -> 0\)], "Input"], Cell[BoxData[ RowBox[{"formal", "=", RowBox[{ RowBox[{ RowBox[{"Solve", "[", RowBox[{\(e\_55 /. TVI[__] -> 1\), ",", InterpretationBox[ StyleBox[\(4\^+\), FontWeight->"Bold"], Schiebe[ 4, "+"], Editable->True]}], "]"}], "[", \([1, 1]\), "]"}], "/.", \(\[Nu]\_2 -> \[Nu]\_2 - 1\)}]}]], "Input"], Cell[BoxData[ \(r\_6552 /. formal\)], "Input"], Cell[BoxData[ \(n\_6552 = OperatorApplyV[r\_6552 /. formal]\)], "Input"], Cell[BoxData[ \(n\_6552[\([2, 4]\)]\)], "Input"], Cell[BoxData[ \(s\_6552 = \(-n\_6552[\([2, 4]\)]\) == \((n\_6552[\([2]\)] - n\_6552[\([2, 4]\)])\)\)], "Input"], Cell[BoxData[ RowBox[{\(f\_6552\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(s\_6552\), ",", "\"\<(6552)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", RowBox[{\(\[CapitalDelta]\_\(2, 4, 6\) === 0\), "&&", RowBox[{ RowBox[{"Expand", "[", RowBox[{ RowBox[{"2", " ", \((\[Nu]\_2 - \[Nu]\_4)\), " ", InterpretationBox[\(m\_4\%2\), Power[ m4, 2]]}], "+", \(\((3\ \[Nu]\_2 - d)\)\ u\_\(2, 4, 6\)\), "+", \(\[Nu]\_2\ u\_\(6, 2, 4\)\)}], "]"}], "=!=", "0"}]}], "]"}]}], "]"}]}]], "Input"], Cell["CheckTVIRecursion not applicable .", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (6552)", "Subsection", CellTags->"T1.6.39.1"], Cell[BoxData[ \(r\_6552 = \[Nu]explicit[e\_52] /. \[CapitalDelta]\_\(2, 4, 6\) -> 0\)], "Input"], Cell[BoxData[ \(n\_6552 = OperatorApplyV[r\_6552]\)], "Input"], Cell[BoxData[ \(n\_6552[\([2, 5]\)]\)], "Input"], Cell[BoxData[ \(s\_6552 = \(-n\_6552[\([2, 5]\)]\) == \((n\_6552[\([2]\)] - n\_6552[\([2, 5]\)])\)\)], "Input"], Cell[BoxData[ RowBox[{\(f\_6552\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(s\_6552\), ",", "\"\<(6552)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", \(\[CapitalDelta]\_\(2, 4, 6\) === 0 && Expand[\(( \(-2\)\ \[Nu]\_2\ m\_4\%2 + 2\ \[Nu]\_4\ m\_4\%2 + d\ u\_\(2, 4, 6\) - 3\ \[Nu]\_2\ u\_\(2, 4, 6\))\)] =!= 0\), "]"}]}], "]"}]}]], "Input"], Cell["CheckTVIRecursion not applicable .", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (6553)", "Subsection", CellTags->"T1.6.40.1"], Cell[BoxData[ \(r\_6553 = \(\(\[Nu]explicit[s\_55] /. u\_\(3, 1, 4\) -> 0\) /. u\_\(6, 2, 4\) -> 0\) /. m\_4 -> 0\)], "Input"], Cell[BoxData[ \(h\_6553 = \(-r\_6553[\([2, 1]\)]\) == \((r\_6553[\([2]\)] - r\_6553[\([2, 1]\)])\)\)], "Input"], Cell[BoxData[ RowBox[{\(f\_6553\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_6553\), ",", "\"\<(6553)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", \(u\_\(6, 2, 4\) === 0 && u\_\(1, 3, 4\) === 0\), "]"}], ",", \(m4 :> 0\)}], "]"}]}]], "Input"], Cell["CheckTVIRecursion not applicable .", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Input (66) ", "Subsection", CellTags->"T1.6.41.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_66\), "=", RowBox[{ RowBox[{"4", InterpretationBox[\(p\^2\), PP], \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox[\(d + 2\), "TraditionalForm"], ")"}]], TVI[ Plus[ 2, d], { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}], "==", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ \(6 d\), "-", \(6 \[Nu]\_1\), "-", \(5 \[Nu]\_2\), "-", \(6 \[Nu]\_3\), "-", \(4 \[Nu]\_4\), "-", RowBox[{"6", \(m\_1\%2\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True]}]}], ")"}], "+", RowBox[{\((u\_\(6, 2, 4\) - 4 m\_2\%2)\), \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True]}], "-", RowBox[{"6", \(m\_3\%2\), \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True]}], "+", RowBox[{"2", \((u\_\(6, 2, 4\) - m\_4\%2)\), \(\[Nu]\_4\), InterpretationBox[ StyleBox[\(4\^+\), FontWeight->"Bold"], Schiebe[ 4, "+"], Editable->True]}], "-", RowBox[{\(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True]}], "-", RowBox[{"2", \(\[Nu]\_4\), InterpretationBox[ StyleBox[\(4\^+\), FontWeight->"Bold"], Schiebe[ 4, "+"], Editable->True], InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}]}], ")"}]}], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_66 = OperatorApplyV[e\_66]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (66)", "Subsection", CellTags->"T1.6.42.1"], Cell[BoxData[ \(h\_66 = s\_66 /. {\[Nu]\_1 :> \[Nu]\_1 - 1, \[Nu]\_2 :> \[Nu]\_2 - 1, \[Nu]\_3 :> \[Nu]\_3 - 1, d :> d - 2}\)], "Input"], Cell[BoxData[ RowBox[{\(f\_66\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_66\), ",", "\"\<(66)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", \(PP =!= 0 && \[Nu]\_1 > 1 && \[Nu]\_2 > 1 && \[Nu]\_3 > 1 && MatchQ[d, _Symbol + _Integer?Positive]\), "]"}]}], "]"}]}]], "Input"], Cell[BoxData[ \(CheckTVIRecursion[f\_66]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (alternative67)", "Subsection", CellTags->"T1.6.43.1"], Cell["\<\ we dereived an alternative formula for Tarasov's (67), but do not save it by \ default.\ \>", "Text"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_67\), "=", RowBox[{ RowBox[{"4", InterpretationBox[\(p\^2\), PP], \(\[Nu]\_1\), \((\[Nu]\_1 + 1)\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox[\(d + 2\), "TraditionalForm"], ")"}]], TVI[ Plus[ 2, d], { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}], " ", "==", RowBox[{ RowBox[{"(", RowBox[{ \((6 d - 6 \[Nu]\_1 - 5 \[Nu]\_2 - 6 \[Nu]\_3 - 4 \[Nu]\_4) \), "-", RowBox[{ "2", \((u\_\(2, 4, 6\) + 3 m\_1\%2)\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True]}], "+", RowBox[{\((u\_\(6, 2, 4\) - 4 m\_2\%2)\), \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True]}], "-", RowBox[{"6", \(m\_3\%2\), \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True]}], "+", RowBox[{"2", \((u\_\(6, 2, 4\) - m\_4\%2)\), \(\[Nu]\_4\), InterpretationBox[ StyleBox[\(4\^+\), FontWeight->"Bold"], Schiebe[ 4, "+"], Editable->True]}], "+", RowBox[{"2", \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}], ")"}]}], "-", RowBox[{\(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True]}], "-", RowBox[{"2", \(\[Nu]\_4\), InterpretationBox[ StyleBox[\(4\^+\), FontWeight->"Bold"], Schiebe[ 4, "+"], Editable->True], InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_67 = OperatorApplyV[e\_67]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (67)", "Subsection", CellTags->"T1.6.44.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_67\), "=", RowBox[{ RowBox[{"4", InterpretationBox[\(p\^2\), PP], \(\[Nu]\_1\), \((\[Nu]\_1 + 1)\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox[\(d + 2\), "TraditionalForm"], ")"}]], TVI[ Plus[ 2, d], { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}], " ", "==", RowBox[{ RowBox[{"(", RowBox[{ \(2 \((2 d - 2 \[Nu]\_1 - 2 \[Nu]\_2 - 2 \[Nu]\_3 - \[Nu]\_4)\)\), "-", RowBox[{ "2", \((u\_\(2, 4, 6\) + 2 m\_1\%2)\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True]}], "+", RowBox[{\(-4\), \(m\_2\%2\), \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True]}], "-", RowBox[{"4", \(m\_3\%2\), \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True]}], "+", RowBox[{"2", \(u\_\(6, 2, 4\)\), \(\[Nu]\_4\), InterpretationBox[ StyleBox[\(4\^+\), FontWeight->"Bold"], Schiebe[ 4, "+"], Editable->True]}], "+", RowBox[{"2", \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}], ")"}]}], "-", RowBox[{"2", \(\[Nu]\_4\), InterpretationBox[ StyleBox[\(4\^+\), FontWeight->"Bold"], Schiebe[ 4, "+"], Editable->True], InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[TextData[Cell[BoxData[ FormBox[ RowBox[{ RowBox[{\(-4\), " ", \(\[Nu]\_2\), " ", InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], StyleBox[ FormBox[\(\[Nu]\_2\), "TraditionalForm"], FontColor->RGBColor[0, 0, 1]], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Plus[ 1, Subscript[ \[Nu], 2]], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True], " ", \(m\_2\%2\)}], "-", RowBox[{"2", " ", \(\[Nu]\_4\), " ", InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], StyleBox[ FormBox[\(\[Nu]\_2\), "TraditionalForm"], FontColor->RGBColor[1, 0, 0]], FormBox[\(\[Nu]\_3\), "TraditionalForm"], StyleBox[ FormBox[\(\[Nu]\_4\), "TraditionalForm"], FontColor->RGBColor[0, 0, 1]]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Plus[ -1, Subscript[ \[Nu], 2]], Subscript[ \[Nu], 3], Plus[ 1, Subscript[ \[Nu], 4]]}], Editable->True]}], "+", RowBox[{ "2", " ", \((2\ d - 2\ \[Nu]\_1 - 2\ \[Nu]\_2 - 2\ \[Nu]\_3 - \[Nu]\_4)\), " ", InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}], "-", RowBox[{ "2", " ", \((m\_2\%2 + m\_4\%2 - p\^2)\), " ", \(\[Nu]\_4\), " ", InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], StyleBox[ FormBox[\(\[Nu]\_4\), "TraditionalForm"], FontColor->RGBColor[0, 0, 1]]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Plus[ 1, Subscript[ \[Nu], 4]]}], Editable->True]}], "-", RowBox[{"4", " ", \(m\_3\%2\), " ", \(\[Nu]\_3\), " ", InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], StyleBox[ FormBox[\(\[Nu]\_3\), "TraditionalForm"], FontColor->RGBColor[0, 0, 1]], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Plus[ 1, Subscript[ \[Nu], 3]], Subscript[ \[Nu], 4]}], Editable->True]}], "-", RowBox[{"2", " ", \(\[Nu]\_1\), " ", InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ StyleBox[ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FontColor->RGBColor[0, 0, 1]], StyleBox[ FormBox[\(\[Nu]\_2\), "TraditionalForm"], FontColor->RGBColor[1, 0, 0]], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Plus[ 1, Subscript[ \[Nu], 1]], Plus[ -1, Subscript[ \[Nu], 2]], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}], "+", RowBox[{"2", " ", \(\[Nu]\_1\), " ", InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ StyleBox[ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FontColor->RGBColor[0, 0, 1]], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], StyleBox[ FormBox[\(\[Nu]\_4\), "TraditionalForm"], FontColor->RGBColor[1, 0, 0]]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Plus[ 1, Subscript[ \[Nu], 1]], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Plus[ -1, Subscript[ \[Nu], 4]]}], Editable->True]}], "-", RowBox[{ "2", " ", \((2\ m\_1\%2 + m\_2\%2 - m\_4\%2 - p\^2)\), " ", \(\[Nu]\_1\), " ", InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ StyleBox[ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FontColor->RGBColor[0, 0, 1]], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Plus[ 1, Subscript[ \[Nu], 1]], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}], "-", RowBox[{ "4", " ", \(p\^2\), " ", \(\[Nu]\_1\), " ", \((\[Nu]\_1 + 1)\), " ", \(\[Nu]\_2\), " ", InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ StyleBox[ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], StyleBox[ FormBox[\(\[Nu]\_2\), "TraditionalForm"], FontColor->RGBColor[0, 0, 1]], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox[\(d + 2\), "TraditionalForm"], ")"}]], TVI[ Plus[ 2, d], { Plus[ 2, Subscript[ \[Nu], 1]], Plus[ 1, Subscript[ \[Nu], 2]], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}]}], TraditionalForm]]]], "Text"], Cell[BoxData[ \(s\_67 = OperatorApplyV[e\_67]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (67)", "Subsection", CellTags->"T1.6.45.1"], Cell[BoxData[ \(h\_67 = s\_67 /. {\[Nu]\_1 :> \[Nu]\_1 - 2, \[Nu]\_2 :> \[Nu]\_2 - 1, d :> d - 2}\)], "Input"], Cell[BoxData[ RowBox[{\(f\_67\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_67\), ",", "\"\<(67)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", \(PP =!= 0 && \[Nu]\_1 > 2 && \[Nu]\_2 > 1 && MatchQ[d, _Symbol + _Integer?Positive]\), "]"}]}], "]"}]}]], "Input"], Cell[BoxData[ \(CheckTVIRecursion[f\_67]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (6713)", "Subsection", CellTags->"T1.6.46.1"], Cell[BoxData[ \(h\_6713 = Interchange[s\_67, 1 \[LeftRightArrow] 3] /. {\[Nu]\_3 :> \[Nu]\_3 - 2, \[Nu]\_2 :> \[Nu]\_2 - 1, d :> d - 2}\)], "Input"], Cell[BoxData[ RowBox[{\(f\_6713\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_6713\), ",", "\"\<(6713)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", \(PP =!= 0 && \[Nu]\_3 > 2 && \[Nu]\_2 > 1 && MatchQ[d, _Symbol + _Integer?Positive]\), "]"}]}], "]"}]}]], "Input"], Cell[BoxData[ \(CheckTVIRecursion[f\_6713]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (68)", "Subsection", CellTags->"T1.6.47.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_68\), "=", RowBox[{ RowBox[{"4", InterpretationBox[\(p\^2\), PP], \(m\_4\%2\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], \(\[Nu]\_2\), \((\[Nu]\_2 + 1)\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox[\(d + 2\), "TraditionalForm"], ")"}]], TVI[ Plus[ 2, d], { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}], "==", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ \((\((m\_1\%2 - m\_3\%2)\) \((2 d - 2 \[Nu]\_1 - \[Nu]\_2 - 2 \[Nu]\_3 - 2 \[Nu]\_4)\) + \(m\_4\%2\) \((2 \[Nu]\_1 + \[Nu]\_2 - 2 \[Nu]\_3)\)) \), "-", RowBox[{\(u\_\(1, 3, 4\)\), RowBox[{"(", RowBox[{ RowBox[{"2", \(m\_1\%2\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True]}], "+", RowBox[{\(u\_\(2, 4, 6\)\), \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True]}]}], ")"}]}], "+", RowBox[{\(u\_\(3, 1, 4\)\), RowBox[{"(", RowBox[{ RowBox[{"2", \(m\_3\%2\), \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True]}], "+", RowBox[{\(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True]}]}], ")"}]}], "-", RowBox[{"2", \(m\_4\%2\), RowBox[{"(", RowBox[{ RowBox[{\(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True]}], "+", RowBox[{\(\[Nu]\_4\), InterpretationBox[ StyleBox[\(4\^+\), FontWeight->"Bold"], Schiebe[ 4, "+"], Editable->True]}]}], ")"}], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True]}], ")"}]}]}], ")"}]}], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"], FormBox[\(\[Nu]\_4\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3], Subscript[ \[Nu], 4]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_68 = OperatorApplyV[e\_68]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (68)", "Subsection", CellTags->"T1.6.48.1"], Cell[BoxData[ \(h\_68 = s\_68 /. {\[Nu]\_1 :> \[Nu]\_1 - 1, \[Nu]\_2 :> \[Nu]\_2 - 2, d :> d - 2}\)], "Input"], Cell[BoxData[ RowBox[{\(f\_68\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_68\), ",", "\"\<(68)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", \(PP =!= 0 && m4 =!= 0 && \[Nu]\_1 > 1 && \[Nu]\_2 > 2 && MatchQ[d, _Symbol + _Integer?Positive]\), "]"}]}], "]"}]}]], "Input"], Cell[BoxData[ \(CheckTVIRecursion[f\_68]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (6813)", "Subsection", CellTags->"T1.6.49.1"], Cell[BoxData[ \(h\_6813 = Interchange[s\_68, 1 \[LeftRightArrow] 3] /. {\[Nu]\_2 :> \[Nu]\_2 - 2, \[Nu]\_3 :> \[Nu]\_3 - 1, d :> d - 2}\)], "Input"], Cell[BoxData[ RowBox[{\(f\_6813\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_6813\), ",", "\"\<(6813)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", \(\(PP =!= 0 && m4 =!= 0\) && \[Nu]\_2 > 2 && \[Nu]\_3 > 1 && MatchQ[d, _Symbol + _Integer?Positive]\), "]"}]}], "]"}]}]], "Input"], Cell[BoxData[ \(CheckTVIRecursion[f\_6813]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (70)", "Subsection", CellTags->"T1.6.50.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_70\), "=", RowBox[{ RowBox[{\((3 d - 10)\), \(\((d - 3)\)\^2\), \(m\_4\%2\), InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox["1", "TraditionalForm"], FormBox["1", "TraditionalForm"], FormBox["1", "TraditionalForm"], FormBox["1", "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, {1, 1, 1, 1}], Editable->True]}], "==", RowBox[{ RowBox[{ FractionBox["1", RowBox[{"4", InterpretationBox[\(p\^2\), PP]}]], RowBox[{"(", RowBox[{ RowBox[{\((3 d - 10)\), \(\[CapitalDelta]\_\(1, 3, 4\)\), RowBox[{"(", RowBox[{\(\[CapitalDelta]\_\(2, 4, 6\)\), "+", RowBox[{\(u\_\(2, 4, 6\)\), RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True]}], ")"}]}]}], ")"}]}], "-", RowBox[{"8", \(\((d - 4)\)\^2\), InterpretationBox[\(p\^2\), PP], \(m\_3\%2\), \(m\_4\%2\), InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True]}]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox["1", "TraditionalForm"], FormBox["1", "TraditionalForm"], FormBox["1", "TraditionalForm"], FormBox["1", "TraditionalForm"]}], RowBox[{"(", FormBox[\(d - 2\), "TraditionalForm"], ")"}]], TVI[ Plus[ -2, d], {1, 1, 1, 1}], Editable->True]}], "+", "\n", "\t\t\t", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{\((d - 3)\), \(m\_4\%2\), RowBox[{"(", RowBox[{ RowBox[{"4", \(m\_1\%2\), \((d - 4)\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True]}], "-", RowBox[{"8", \((d - 3)\), \(m\_2\%2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True]}], "+", RowBox[{\((3 d - 10)\), \((d - 3)\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True]}]}], ")"}]}], "+", RowBox[{\(u\_\(6, 2, 4\)\), RowBox[{"(", RowBox[{ RowBox[{ \(1\/2\), \((3 d - 10)\), \(u\_\(1, 3, 4\)\), RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], "-", InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True]}], ")"}]}], "+", RowBox[{\((d - 2)\), \((d - 3)\), \(m\_4\%2\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True]}]}], ")"}], InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True]}], "-", RowBox[{\(m\_4\%2\), RowBox[{"(", RowBox[{ RowBox[{\(\((d - 4)\)\^2\), \(u\_\(1, 3, 4\)\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True]}], "+", RowBox[{\((3 d - 10)\), \(u\_\(4, 1, 3\)\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True]}]}], ")"}], InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True]}]}], ")"}], InterpretationBox[ StyleBox[\(4\^-\), FontWeight->"Bold"], Schiebe[ 4, "-"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox["1", "TraditionalForm"], FormBox["1", "TraditionalForm"], FormBox["1", "TraditionalForm"], FormBox["1", "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, {1, 1, 1, 1}], Editable->True]}], "-", RowBox[{\((d - 3)\), \(m\_4\%2\), RowBox[{"(", RowBox[{ RowBox[{"4", \((d - 4)\), \(m\_1\%2\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True]}], "+", RowBox[{\((d - 2)\), RowBox[{"(", RowBox[{ RowBox[{\(u\_\(6, 2, 4\)\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True]}], "-", RowBox[{"2", \(m\_4\%2\), InterpretationBox[ StyleBox[\(4\^+\), FontWeight->"Bold"], Schiebe[ 4, "+"], Editable->True]}]}], ")"}]}]}], ")"}], InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox["1", "TraditionalForm"], FormBox["1", "TraditionalForm"], FormBox["1", "TraditionalForm"], FormBox["1", "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, {1, 1, 1, 1}], Editable->True]}], "+", RowBox[{\(1\/2\), \((3 d - 10)\), \(u\_\(1, 3, 4\)\), RowBox[{"(", RowBox[{ RowBox[{\(u\_\(6, 2, 4\)\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True]}], "-", RowBox[{"2", \(m\_4\%2\), InterpretationBox[ StyleBox[\(4\^+\), FontWeight->"Bold"], Schiebe[ 4, "+"], Editable->True]}]}], ")"}], RowBox[{"(", RowBox[{ RowBox[{ InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True], InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True]}], "-", RowBox[{ InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["V", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox["1", "TraditionalForm"], FormBox["1", "TraditionalForm"], FormBox["1", "TraditionalForm"], FormBox["1", "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TVI[ d, {1, 1, 1, 1}], Editable->True]}]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_70 = OperatorApplyV[e\_70]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (70)", "Subsection", CellTags->"T1.6.51.1"], Cell[BoxData[ \(h\_70 = s\_70\)], "Input"], Cell[BoxData[ RowBox[{\(f\_70\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_70\), ",", "\"\<(70)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", \(\(m4 =!= 0\ && \ PP =!= 0\) && MatchQ[d, _Symbol + _Integer?Positive]\), "]"}]}], "]"}]}]], "Input"], Cell["\<\ CheckTVIRecursion not applicable for special indices since A's and B's appear .\ \>", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Input (71)", "Subsection", CellTags->"T1.6.52.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]], " and ", Cell[BoxData[ \(TraditionalForm\`\[Nu]\_1, \[Nu]\_2 > 0\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_71\), "=", RowBox[{ RowBox[{"2", \(D\_\(1, 2, 3\)\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}], "==", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"2", \(h\_\(1, 2, 3\)\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True]}], "+", RowBox[{"2", \(h\_\(2, 1, 3\)\), \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True]}], "+", RowBox[{ "4", \(m\_3\%2\), \(\[Sigma]\_\(1, 2, 3\)\), \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True]}], "+", RowBox[{\(m\_3\%2\), \(\[Phi]\_\(2, 1, 3\)\), \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True], InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True]}], "+", RowBox[{\(m\_3\%2\), \(\[Phi]\_\(1, 2, 3\)\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True], InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}], "-", RowBox[{"2", \(\[Rho]\_\(1, 2, 3\)\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}], "+", \(\(1\/2\) \(\[CapitalSigma]\_3\) \((d - \[Nu]\_1 - \[Nu]\_2 - \[Nu]\_3)\) \[Phi]\_\(3, 2, 1\)\)}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_71 = OperatorApplyJ[e\_71]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (71)", "Subsection", CellTags->"T1.6.53.1"], Cell[BoxData[ \(h\_71 = \(\[Nu]explicit[s\_71] /. \[Nu]\_1 -> \[Nu]\_1 - 1\) /. \[Nu]\_2 -> \[Nu]\_2 - 1\)], "Input"], Cell[BoxData[ \(f\_71 = MakeFun[h\_71, "\<(71)\>", IFF[\[Nu]\_1 > 1 && \[Nu]\_2 > 1 && D\_\(1, 2, 3\) =!= 0]]\)], "Input"], Cell[BoxData[ \(CheckTJIRecursion[f\_71]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (7123)", "Subsection", CellTags->"T1.6.54.1"], Cell[BoxData[ \(h\_7123 = \(Interchange[s\_71, 2 \[LeftRightArrow] 3] /. \[Nu]\_1 -> \[Nu]\_1 - 1\) /. \[Nu]\_3 -> \[Nu]\_3 - 1\)], "Input"], Cell[BoxData[ \(f\_7123 = MakeFun[h\_7123, "\<(7123)\>", IFF[\[Nu]\_1 > 1 && \[Nu]\_3 > 1 && D\_\(1, 3, 2\) =!= 0]]\)], "Input"], Cell[BoxData[ \(CheckTJIRecursion[f\_7123]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (7113)", "Subsection", CellTags->"T1.6.55.1"], Cell[BoxData[ \(h\_7113 = \(Interchange[s\_71, 1 \[LeftRightArrow] 3] /. \[Nu]\_2 -> \[Nu]\_2 - 1\) /. \[Nu]\_3 -> \[Nu]\_3 - 1\)], "Input"], Cell[BoxData[ \(f\_7113 = MakeFun[h\_7113, "\<(7113)\>", IFF[\[Nu]\_2 > 1 && \[Nu]\_3 > 1 && D\_\(3, 2, 1\) =!= 0]]\)], "Input"], Cell[BoxData[ \(CheckTJIRecursion[f\_7113]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (78)", "Subsection", CellTags->"T1.6.56.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]], " and ", Cell[BoxData[ \(TraditionalForm\`\[Nu]\_1 > 0\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_78\), "=", RowBox[{ RowBox[{ "2", \(m\_1\%2\), " ", \(D\_\(1, 2, 3\)\), \(\[Nu]\_1\), \((\[Nu]\_1 + 1)\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}], "==", RowBox[{ RowBox[{"(", RowBox[{ \(\(-\[CapitalSigma]\_3\) \((d - \[Nu]\_1 - \[Nu]\_2 - \[Nu]\_3)\) \[Rho]\_\(1, 2, 3\)\), "+", RowBox[{ \(m\_2\%2\), \(m\_3\%2\), \(\[Phi]\_\(1, 2, 3\)\), \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True], InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True]}], "+", RowBox[{ \(m\_1\%2\), \(m\_3\%2\), \(\[Phi]\_\(2, 1, 3\)\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True], InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}], "+", RowBox[{ \(m\_1\%2\), \(m\_2\%2\), \(\[Phi]\_\(3, 1, 2\)\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}], "+", RowBox[{ \((d - 2 - 2 \[Nu]\_1)\), \(D\_\(1, 2, 3\)\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True]}], "+", RowBox[{\(m\_1\%2\), \(S\_\(1, 2, 3\)\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True]}], "+", RowBox[{\(m\_2\%2\), \(S\_\(2, 1, 3\)\), \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True]}], "+", RowBox[{\(m\_3\%2\), \(S\_\(3, 1, 2\)\), \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True]}]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_78 = OperatorApplyJ[e\_78]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (78)", "Subsection", CellTags->"T1.6.57.1"], Cell[BoxData[ \(h\_78 = \[Nu]explicit[s\_78] /. \[Nu]\_1 -> \[Nu]\_1 - 2\)], "Input"], Cell[BoxData[ \(f\_78 = MakeFun[h\_78, "\<(78)\>", IFF[\(\[Nu]\_1 > 2 && m1 =!= 0\) && D\_\(1, 2, 3\) =!= 0]]\)], "Input"], Cell[BoxData[ \(CheckTJIRecursion[f\_78]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (80)", "Subsection", CellTags->"T1.6.58.1"], Cell[TextData[{ Cell[BoxData[ \(m\_1\%2 == 0\)]], " and ", Cell[BoxData[ \(TraditionalForm\`\[Nu]\_1 > 0\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_80\), "=", RowBox[{ RowBox[{ \(\[Nu]\_1\), " ", \((d - 2\ \[Nu]\_1 - 2)\), \(\[CapitalDelta]\_\(2, 3, 6\)\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}], "==", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{\(-4\), \(m\_2\%2\), \(m\_3\%2\), \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True], InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True]}], "+", "\n", "\t\t\t\t", RowBox[{"2", \(m\_2\%2\), RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ InterpretationBox[\(p\^2\), PP], "-", \(m\_2\%2\)}], ")"}], \((2 d - 2 \[Nu]\_1 - \[Nu]\_2 - 2 \[Nu]\_3 - 1) \)}], "-", \(\(m\_3\%2\) \((2 \[Nu]\_1 - \[Nu]\_2 - 1)\)\)}], ")"}], \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True]}], "+", "\n", "\t\t\t ", RowBox[{"2", " ", \(m\_3\%2\), RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ InterpretationBox[\(p\^2\), PP], "-", \(m\_3\%2\)}], ")"}], \((2 d - 2 \[Nu]\_1 - 2 \[Nu]\_2 - \[Nu]\_3 - 1) \)}], "-", \(\(m\_2\%2\) \((2 \[Nu]\_1 - \[Nu]\_3 - 1)\)\)}], ")"}], \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True]}], "-", "\n", "\t\t\t\t", \(\(\[CapitalSigma]\_3\) \((d - \[Nu]\_1 - \[Nu]\_2 - \[Nu]\_3)\) u\_\(6, 2, 3\)\)}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_80 = OperatorApplyJ[e\_80]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (80)", "Subsection", CellTags->"T1.6.59.1"], Cell[BoxData[ \(h\_80 = \[Nu]explicit[s\_80] /. \[Nu]\_1 \[Rule] \[Nu]\_1 - 1\)], "Input"], Cell[BoxData[ \(f\_80 = MakeFun[h\_80, "\<(80)\>", IFF[\[Nu]\_1 > 1 && \[CapitalDelta]\_\(2, 3, 6\) =!= 0], m1 :> 0]\)], "Input"], Cell[BoxData[ \(CheckTJIRecursion[f\_80]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (81)", "Subsection", CellTags->"T1.6.60.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]], "and ", Cell[BoxData[ \(TraditionalForm\`\[Nu]\_1, \[Nu]\_2 > 0\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_81\), "=", RowBox[{ RowBox[{ InterpretationBox[\(p\^2\), PP], \((\[CapitalSigma]\_3 + 2)\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox[\(d + 2\), "TraditionalForm"], ")"}]], TJI[ Plus[ 2, d], { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}], "==", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ InterpretationBox[\(p\^2\), PP], \((d - 2 \[Nu]\_3)\)}], "+", \(\(m\_1\%2\) \((d - \[Nu]\_1 - 2 \[Nu]\_2)\)\), "+", \(\(m\_2\%2\) \((d - 2 \[Nu]\_1 - \[Nu]\_2)\)\), "-", \(2 \( m\_3\%2\) \((d - \[Nu]\_1 - \[Nu]\_2 - \[Nu]\_3)\)\), "-", RowBox[{"2", \(m\_3\%2\), RowBox[{"(", RowBox[{ InterpretationBox[\(p\^2\), PP], "-", \(m\_3\%2\)}], ")"}], \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True]}], "+", RowBox[{\(m\_1\%2\), RowBox[{"(", RowBox[{ InterpretationBox[\(p\^2\), PP], "-", \(m\_1\%2\), "-", \(3 m\_2\%2\), "+", \(3 m\_3\%2\), "-", InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True], "+", InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}], ")"}], \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True]}], "+", RowBox[{\(m\_2\%2\), RowBox[{"(", RowBox[{ InterpretationBox[\(p\^2\), PP], "-", \(3 m\_1\%2\), "-", \(m\_2\%2\), "+", \(3 m\_3\%2\), "-", InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True], "+", InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}], ")"}], \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True]}]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_81 = OperatorApplyJ[e\_81]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (81)", "Subsection", CellTags->"T1.6.61.1"], Cell[BoxData[ \(h\_81 = \(\(\[Nu]explicit[s\_81] /. \[Nu]\_1 -> \[Nu]\_1 - 1\) /. \[Nu]\_2 -> \[Nu]\_2 - 1\) /. d -> d - 2\)], "Input"], Cell[BoxData[ \(f\_81 = MakeFun[h\_81, "\<(81)\>", IFF[PP =!= 0 && \[Nu]\_1 > 1 && \[Nu]\_2 > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]\)], "Input"], Cell[BoxData[ \(CheckTJIRecursion[f\_81]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (8123)", "Subsection", CellTags->"T1.6.62.1"], Cell[BoxData[ \(h\_8123 = \(\(Interchange[s\_81, 2 \[LeftRightArrow] 3] /. \[Nu]\_1 -> \[Nu]\_1 - 1\) /. \[Nu]\_3 -> \[Nu]\_3 - 1\) /. d -> d - 2\)], "Input"], Cell[BoxData[ \(f\_8123 = MakeFun[h\_8123, "\<(8123)\>", IFF[PP =!= 0 && \[Nu]\_1 > 1 && \[Nu]\_3 > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]\)], "Input"], Cell[BoxData[ \(CheckTJIRecursion[f\_8123]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (8113)", "Subsection", CellTags->"T1.6.63.1"], Cell[BoxData[ \(h\_8113 = \(\(Interchange[s\_81, 1 \[LeftRightArrow] 3] /. \[Nu]\_2 \[Rule] \[Nu]\_2 - 1\) /. \[Nu]\_3 \[Rule] \[Nu]\_3 - 1\) /. d \[Rule] d - 2\)], "Input"], Cell[BoxData[ \(f\_8113 = MakeFun[h\_8113, "\<(8113)\>", IFF[PP =!= 0 && \[Nu]\_2 > 1 && \[Nu]\_3 > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]\)], "Input"], Cell[BoxData[ \(CheckTJIRecursion[f\_8113]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (82)", "Subsection", CellTags->"T1.6.64.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]], "and ", Cell[BoxData[ \(TraditionalForm\`\[Nu]\_1 > 0\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_82\), "=", RowBox[{ RowBox[{ RowBox[{ RowBox[{"-", InterpretationBox[\(p\^2\), PP]}], \(m\_1\%2\), \((\[CapitalSigma]\_3 + 2)\), \(\[Nu]\_1\), \((\[Nu]\_1 + 1)\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox[\(d + 2\), "TraditionalForm"], ")"}]], TJI[ Plus[ 2, d], { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}], "+", RowBox[{\(1\/2\), InterpretationBox[\(p\^2\), PP], \((\[CapitalSigma]\_3 + 2)\), \((\[CapitalSigma]\_3 + 4)\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox[\(d + 2\), "TraditionalForm"], ")"}]], TJI[ Plus[ 2, d], { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}]}], "==", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{\(-\(1\/2\)\), SuperscriptBox[ RowBox[{"(", InterpretationBox[\(p\^2\), PP], ")"}], "2"], \((d + 2 \[Nu]\_1 - 2 \[Nu]\_2 - 2 \[Nu]\_3)\)}], "+", RowBox[{\(1\/2\), InterpretationBox[\(p\^2\), PP], \((\(m\_1\%2\) \((6 \[Nu]\_1 + 6 \[Nu]\_2 + 6 \[Nu]\_3 - 7 d) \) + \(m\_2\%2\) \((7 d - 2 \[Nu]\_1 - 4 \[Nu]\_2 - 10 \[Nu]\_3) \) + \(m\_3\%2\) \((7 d - 2 \[Nu]\_1 - 10 \[Nu]\_2 - 4 \[Nu]\_3)\)) \)}], "+", \(\(\((m\_2\%2)\)\^2\) \((d - 2 \[Nu]\_1 - \[Nu]\_2)\)\), "+", \(\(\((m\_3\%2)\)\^2\) \((d - 2 \[Nu]\_1 - \[Nu]\_3)\)\), "+", \(\(m\_1\%2\) \(m\_2\%2\) \((d - \[Nu]\_1 - 2 \[Nu]\_2)\)\), "+", \(\(m\_1\%2\) \(m\_3\%2\) \((d - \[Nu]\_1 - 2 \[Nu]\_3)\)\), "-", \(4 \( m\_2\%2\) \(m\_3\%2\) \((d - \[Nu]\_1 - \[Nu]\_2 - \[Nu]\_3)\)\), "-", RowBox[{\(m\_1\%2\), RowBox[{"(", RowBox[{ RowBox[{"2", SuperscriptBox[ RowBox[{"(", InterpretationBox[\(p\^2\), PP], ")"}], "2"]}], "-", RowBox[{ InterpretationBox[\(p\^2\), PP], \((2 m\_1\%2 + m\_2\%2 + m\_3\%2)\)}], "+", \(\(m\_1\%2\) \((m\_2\%2 + m\_3\%2)\)\), "+", \(3 \((m\_2\%2 - m\_3\%2)\)\^2\)}], ")"}], \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True]}], "+", RowBox[{\(m\_2\%2\), RowBox[{"(", RowBox[{ SuperscriptBox[ RowBox[{"(", InterpretationBox[\(p\^2\), PP], ")"}], "2"], "+", RowBox[{ RowBox[{"(", RowBox[{ InterpretationBox[\(p\^2\), PP], "-", \(m\_2\%2\)}], ")"}], RowBox[{"(", RowBox[{\(3 m\_1\%2\), "-", \(5 m\_3\%2\), "+", InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}], ")"}]}], "-", \(\((m\_2\%2)\)\^2\)}], ")"}], \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True]}], "+", RowBox[{\(m\_3\%2\), RowBox[{"(", RowBox[{ SuperscriptBox[ RowBox[{"(", InterpretationBox[\(p\^2\), PP], ")"}], "2"], "+", RowBox[{ RowBox[{"(", RowBox[{ InterpretationBox[\(p\^2\), PP], "-", \(m\_3\%2\)}], ")"}], RowBox[{"(", RowBox[{\(3 m\_1\%2\), "-", \(5 m\_2\%2\), "+", InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}], ")"}]}], "-", \(\((m\_3\%2)\)\^2\)}], ")"}], \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True]}], "-", RowBox[{\(1\/2\), InterpretationBox[\(p\^2\), PP], \((\[CapitalSigma]\_3 + 2)\), RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}], ")"}]}], "-", RowBox[{\(m\_1\%2\), \((m\_2\%2 - m\_3\%2)\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}], ")"}]}]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(r\_82 = OperatorApplyJ[e\_82]\)], "Input"], Cell[BoxData[ \(r\_82[\([1, 1]\)]\)], "Input"], Cell[BoxData[ \(\(s\_82 = \((r\_82[\([1, 2]\)] == \(-r\_82[\([1, 1]\)]\) + r\_82[\([2]\)])\); \)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (82)", "Subsection", CellTags->"T1.6.65.1"], Cell[BoxData[ \(h\_82 = \(\[Nu]explicit[s\_82] /. \[Nu]\_1 -> \[Nu]\_1 - 2\) /. d -> d - 2\)], "Input"], Cell[BoxData[ \(f\_82 = MakeFun[h\_82, "\<(82)\>", IFF[\(PP =!= 0 && \[Nu]\_1 > 2 && m1 =!= 0\) && MatchQ[d, _Symbol + _Integer?Positive]]]\)], "Input"], Cell[BoxData[ \(CheckTJIRecursion[f\_82]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (8213)", "Subsection", CellTags->"T1.6.66.1"], Cell[BoxData[ \(h\_8213 = \(Interchange[s\_82, 1 \[LeftRightArrow] 3] /. \[Nu]\_3 -> \[Nu]\_3 - 2\) /. d -> d - 2\)], "Input"], Cell[BoxData[ \(f\_8213 = MakeFun[h\_8213, "\<(8213)\>", IFF[\(PP =!= 0 && m3 =!= 0\) && \[Nu]\_3 > 2 && MatchQ[d, _Symbol + _Integer?Positive]]]\)], "Input"], Cell[BoxData[ \(CheckTJIRecursion[f\_8213]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (8212)", "Subsection", CellTags->"T1.6.67.1"], Cell[BoxData[ \(h\_8212 = \(Interchange[s\_82, 1 \[LeftRightArrow] 2] /. \[Nu]\_2 -> \[Nu]\_2 - 2\) /. d -> d - 2\)], "Input"], Cell[BoxData[ \(f\_8212 = MakeFun[h\_8212, "\<(8212)\>", IFF[\(PP =!= 0 && \[Nu]\_2 > 2 && m2 =!= 0\) && MatchQ[d, _Symbol + _Integer?Positive]]]\)], "Input"], Cell[BoxData[ \(CheckTJIRecursion[f\_8212]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (83)", "Subsection", CellTags->"T1.6.68.1"], Cell[TextData[{ Cell[BoxData[ \(m\_1\%2 == 0\)]], " and ", Cell[BoxData[ \(TraditionalForm\`\[Nu]\_1 > 0\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_83\), "=", RowBox[{ RowBox[{ InterpretationBox[\(p\^2\), PP], \((\[CapitalSigma]\_3 + 2)\), \((\[CapitalSigma]\_3 + 4)\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox[\(d + 2\), "TraditionalForm"], ")"}]], TJI[ Plus[ 2, d], { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}], "==", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox[ RowBox[{"(", InterpretationBox[\(p\^2\), PP], ")"}], "2"]}], \((d + 2 \[Nu]\_1 - 2 \[Nu]\_2 - 2 \[Nu]\_3)\)}], "+", RowBox[{ InterpretationBox[\(p\^2\), PP], \((\(m\_2\%2\) \((7 d - 2 \[Nu]\_1 - 4 \[Nu]\_2 - 10 \[Nu]\_3) \) + \(m\_3\%2\) \((7 d - 2 \[Nu]\_1 - 10 \[Nu]\_2 - 4 \[Nu]\_3)\)) \)}], "+", \(2 \(\((m\_2\%2)\)\^2\) \((d - 2 \[Nu]\_1 - \[Nu]\_2)\)\), "+", \(2 \(\((m\_3\%2)\)\^2\) \((d - 2 \[Nu]\_1 - \[Nu]\_3)\)\), "-", \(8 \( m\_2\%2\) \(m\_3\%2\) \((d - \[Nu]\_1 - \[Nu]\_2 - \[Nu]\_3)\)\), "+", RowBox[{"2", \(m\_2\%2\), RowBox[{"(", RowBox[{ SuperscriptBox[ RowBox[{"(", InterpretationBox[\(p\^2\), PP], ")"}], "2"], "-", RowBox[{ RowBox[{"(", RowBox[{ InterpretationBox[\(p\^2\), PP], "-", \(m\_2\%2\)}], ")"}], RowBox[{"(", RowBox[{\(5 m\_3\%2\), "-", InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True], "+", InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}], ")"}]}], "-", \(\((m\_2\%2)\)\^2\)}], ")"}], \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True]}], "+", RowBox[{"2", \(m\_3\%2\), RowBox[{"(", RowBox[{ SuperscriptBox[ RowBox[{"(", InterpretationBox[\(p\^2\), PP], ")"}], "2"], "-", RowBox[{ RowBox[{"(", RowBox[{ InterpretationBox[\(p\^2\), PP], "-", \(m\_3\%2\)}], ")"}], RowBox[{"(", RowBox[{\(5 m\_2\%2\), "-", InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True], "+", InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}], ")"}]}], "-", \(\((m\_3\%2)\)\^2\)}], ")"}], \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True]}], "-", RowBox[{ InterpretationBox[\(p\^2\), PP], \((\[CapitalSigma]\_3 + 2)\), RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}], ")"}]}]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_83 = OperatorApplyJ[e\_83]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (83)", "Subsection", CellTags->"T1.6.69.1"], Cell[BoxData[ \(h\_83 = \(\[Nu]explicit[s\_83] /. \[Nu]\_1 -> \[Nu]\_1 - 1\) /. d -> d - 2\)], "Input"], Cell[BoxData[ \(f\_83 = MakeFun[h\_83, "\<(83)\>", IFF[PP =!= 0 && \[Nu]\_1 > 1 && MatchQ[d, _Symbol + _Integer?Positive]], m1 :> 0]\)], "Input"], Cell[BoxData[ \(CheckTJIRecursion[f\_83]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (87)", "Subsection", CellTags->"T1.6.70.1"], Cell[CellGroupData[{ Cell["(88)", "Subsubsection", CellTags->"T1.6.70.1.1"], Cell[BoxData[ \(\(t\_1 = m\_1\%2 + m\_2\%2 + m\_3\%2; \)\)], "Input"], Cell[BoxData[ \(\(t\_2 = 3 \((m\_1\%4 + m\_2\%4 + m\_3\%4)\) + 2 \((\(m\_1\%2\) m\_2\%2 + \(m\_1\%2\) m\_3\%2 + \(m\_2\%2\) m\_3\%2) \); \)\)], "Input"], Cell[BoxData[ \(\(t\_3 = \(m\_1\%2\) \((m\_1\%4 - m\_2\%4 - m\_3\%4)\) + \(m\_2\%2\) \((m\_2\%4 - m\_1\%4 - m\_3\%4)\) + \(m\_3\%2\) \((m\_3\%4 - m\_1\%4 - m\_2\%4)\) + 10 \( m\_1\%2\) \(m\_2\%2\) m\_3\%2; \)\)], "Input"], Cell[BoxData[ RowBox[{ RowBox[{\(f[\[Mu]1_, \[Mu]2_, \ \[Mu]3_]\), ":=", RowBox[{"\[Mu]1", RowBox[{"(", RowBox[{ InterpretationBox[\(p\^2\), PP], "-", "\[Mu]1"}], ")"}], RowBox[{"(", RowBox[{ RowBox[{\(-2\), \((d - 4)\), SuperscriptBox[ RowBox[{"(", InterpretationBox[\(p\^2\), PP], ")"}], "2"]}], "+", RowBox[{ InterpretationBox[\(p\^2\), PP], \((4 \( t\_1\) \((5 d - 18)\) - 24 \[Mu]1 \((2 d - 7)\)) \)}], "-", \(2 \((4 d - 13)\) t\_1\^2\), "+", \(2 \((9 d - 31)\) t\_2\), "-", \(24 \[Mu]2\ \[Mu]3 \((4 d - 13)\)\), "-", \(24\ \(\[Mu]1\^2\) \((2 d - 7)\)\)}], ")"}]}]}], ";"}]], "Input"], Cell[BoxData[ \(f\_\(1, 2, 3\) = f[m\_1\%2, m\_2\%2, m\_3\%2]; \n f\_\(2, 1, 3\) = f[m\_2\%2, m\_1\%2, m\_3\%2]; \n f\_\(3, 2, 1\) = f[m\_3\%2, m\_2\%2, m\_1\%2]; \)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["(89)", "Subsubsection", CellTags->"T1.6.70.2.1"], Cell[BoxData[ RowBox[{ RowBox[{\(g[\[Mu]1_, \[Mu]2_, \ \[Mu]3_]\), ":=", RowBox[{\(\(\[Mu]1\ \[Mu]2\)\/\(d - 4\)\), RowBox[{"(", RowBox[{ RowBox[{"4", \((d - 4)\), SuperscriptBox[ RowBox[{"(", InterpretationBox[\(p\^2\), PP], ")"}], "2"]}], "-", RowBox[{"4", \((7 d - 24)\), InterpretationBox[\(p\^2\), PP], \((3 \[Mu]3 - 2 t\_1)\)}], "-", \(\(t\_1\^2\) \((23 d - 80)\)\), "+", \(\(t\_2\) \((9 d - 32)\)\), "-", \(12 \( \[Mu]3\^2\) \((d - 4)\)\), "+", \(12 \[Mu]1\ \[Mu]2\ \((7 d - 24)\)\)}], ")"}]}]}], ";"}]], "Input"], Cell[BoxData[ \(g\_\(1, 2, 3\) = g[m\_1\%2, m\_2\%2, m\_3\%2]; \n g\_\(1, 3, 2\) = g[m\_1\%2, m\_3\%2, m\_2\%2]; \n g\_\(2, 3, 1\) = g[m\_2\%2, m\_3\%2, m\_1\%2]; \)], "Input"], Cell[BoxData[ \(g\_\(1, 2, 3\)\)], "Input"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]], " " }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_87\), "=", RowBox[{ RowBox[{"3", InterpretationBox[\(p\^2\), PP], \((d - 3)\), \((d - 4)\), \((3 d - 8)\), \((3 d - 10)\), InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox["1", "TraditionalForm"], FormBox["1", "TraditionalForm"], FormBox["1", "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, {1, 1, 1}], Editable->True]}], "==", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{\(\((d - 4)\)\^2\), SuperscriptBox[ RowBox[{"(", InterpretationBox[\(p\^2\), PP], ")"}], "3"]}], "-", RowBox[{"2", SuperscriptBox[ RowBox[{"(", InterpretationBox[\(p\^2\), PP], ")"}], "2"], \(t\_1\), \((d - 4)\), \((6 d - 23)\)}], "+", RowBox[{ InterpretationBox[\(p\^2\), PP], \((5 \( t\_1\^2\) \((15 d\^2 - 117 d + 224)\) - \(t\_2\) \((42 d\^2 - 331 d + 640)\))\)}], "-", \(\(1\/4\) \((d - 5)\) \((\(t\_3\) \((27 d - 90)\) - \(t\_1\) \(t\_2\) \((3 d - 2)\) - 2 \( t\_1\^3\) \((5 d - 26)\))\)\), "+", RowBox[{\(f\_\(1, 2, 3\)\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True]}], "+", RowBox[{\(f\_\(2, 1, 3\)\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True]}], "+", RowBox[{\(f\_\(3, 2, 1\)\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True]}], "+", RowBox[{\(g\_\(1, 2, 3\)\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}], "+", RowBox[{\(g\_\(1, 3, 2\)\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True], InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True]}], "+", RowBox[{\(g\_\(2, 3, 1\)\), InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True], InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True]}]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox["1", "TraditionalForm"], FormBox["1", "TraditionalForm"], FormBox["1", "TraditionalForm"]}], RowBox[{"(", FormBox[\(d - 2\), "TraditionalForm"], ")"}]], TJI[ Plus[ -2, d], {1, 1, 1}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_87 = OperatorApplyJ[e\_87]\)], "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (87)", "Subsection", CellTags->"T1.6.71.1"], Cell[BoxData[ \(h\_87 = s\_87\)], "Input"], Cell[BoxData[ \(\(f\_87 = MakeFun[h\_87, "\<(87)\>", IFF[PP =!= 0 && MatchQ[d, _Symbol + _Integer?Positive]]]; \)\)], "Input"], Cell["CheckTJIRecursion not applicable.", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Input (90)", "Subsection", CellTags->"T1.6.72.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]], " " }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_90\), "=", RowBox[{ RowBox[{"3", InterpretationBox[\(p\^2\), PP], \((d - 3)\), \((d - 4)\), \((3 d - 10)\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox["1", "TraditionalForm"], FormBox["1", "TraditionalForm"], FormBox["1", "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, {1, 1, 1}], Editable->True]}], "==", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{\(-m\_1\%2\), RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", InterpretationBox[\(p\^2\), PP], ")"}], "2"], \((7 d - 24)\)}], "-", RowBox[{"2", InterpretationBox[\(p\^2\), PP], \((\((4 d - 15)\) t\_1 - \((d - 5)\) m\_1\%2)\)}], "+", \(\(3\/2\) \((d - 5)\) t\_1\^2\), "+", \(\(5\/2\) \((d - 3)\) t\_2\), "-", \(2 \((5 d - 17)\) \((m\_1\%2)\)\^2\), "-", \(2 \((13 d - 45)\) \(m\_2\%2\) m\_3\%2\)}], ")"}], InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True]}], "+", "\n", "\t\t\t\t", RowBox[{"2", \(m\_2\%2\), RowBox[{"(", RowBox[{ InterpretationBox[\(p\^2\), PP], "-", \(m\_2\%2\)}], ")"}], RowBox[{"(", RowBox[{ RowBox[{\((d - 3)\), RowBox[{"(", RowBox[{ InterpretationBox[\(p\^2\), PP], "+", \(m\_2\%2\), "-", \(5 m\_3\%2\)}], ")"}]}], "+", \(\((7 d - 25)\) m\_1\%2\)}], ")"}], InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True]}], "+", "\n", "\t\t\t\t", RowBox[{"2", \(m\_3\%2\), RowBox[{"(", RowBox[{ InterpretationBox[\(p\^2\), PP], "-", \(m\_3\%2\)}], ")"}], RowBox[{"(", RowBox[{ RowBox[{\((d - 3)\), RowBox[{"(", RowBox[{ InterpretationBox[\(p\^2\), PP], "-", \(5 m\_2\%2\), "+", \(m\_3\%2\)}], ")"}]}], "+", \(\((7 d - 25)\) m\_1\%2\)}], ")"}], InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True]}], "-", "\n", "\t\t\t\t", RowBox[{\((d - 3)\), \((d - 4)\), SuperscriptBox[ RowBox[{"(", InterpretationBox[\(p\^2\), PP], ")"}], "2"]}], "+", RowBox[{ InterpretationBox[\(p\^2\), PP], \((\((7 d - 30)\) \((d - 3)\) t\_1 - \((7 d - 31)\) \((3 d - 10)\) m\_1\%2)\)}], "+", \(\(1\/4\) \((d - 5)\) \((\((17 d - 66)\) t\_1\^2 - \((3 d - 14)\) t\_2 - 4 \((3 d - 10)\) \((\((m\_1\%2)\)\^2 + 5 \( m\_2\%2\) m\_3\%2)\))\)\), "+", "\t", RowBox[{\(2\/\(d - 4\)\), RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ InterpretationBox[\(p\^2\), PP], "+", \(m\_2\%2\)}], ")"}], \((7 d - 24)\)}], "+", \(\((d - 4)\) m\_1\%2\), "-", \(\((5 d - 18)\) m\_3\%2\)}], ")"}], \(m\_1\%2\), \(m\_2\%2\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}], "+", "\n", "\t\t\t\t\t\t", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ InterpretationBox[\(p\^2\), PP], "+", \(m\_3\%2\)}], ")"}], \((7 d - 24)\)}], "+", \(\((d - 4)\) m\_1\%2\), "-", \(\((5 d - 18)\) m\_2\%2\)}], ")"}], \(m\_1\%2\), \(m\_3\%2\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True], InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True]}], "-", "\n", "\t\t\t\t\t\t", RowBox[{"2", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ InterpretationBox[\(p\^2\), PP], "+", \(m\_2\%2\), "+", \(m\_3\%2\)}], ")"}], \((d - 3)\)}], "+", \(\((d - 4)\) m\_1\%2\)}], ")"}], \(m\_2\%2\), \(m\_3\%2\), InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True], InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True]}]}], ")"}]}]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox["1", "TraditionalForm"], FormBox["1", "TraditionalForm"], FormBox["1", "TraditionalForm"]}], RowBox[{"(", FormBox[\(d - 2\), "TraditionalForm"], ")"}]], TJI[ Plus[ -2, d], {1, 1, 1}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_90 = OperatorApplyJ[e\_90]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (90)", "Subsection", CellTags->"T1.6.73.1"], Cell[BoxData[ \(\(h\_90 = s\_90; \)\)], "Input"], Cell[BoxData[ \(f\_90 = MakeFun[h\_90, "\<(90)\>", IFF[PP =!= 0 && MatchQ[d, _Symbol + _Integer?Positive]]]\)], "Input"], Cell["CheckTJIRecursion not applicable.", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Input (91)", "Subsection", CellTags->"T1.6.74.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_91.1\), "=", " ", RowBox[{ RowBox[{\((d - 2)\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["K", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TKI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}], "==", RowBox[{ RowBox[{"(", RowBox[{\(-u\_\(1, 2, 3\)\), "-", InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True], "+", InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True], "+", InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["K", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox[\(d - 2\), "TraditionalForm"], ")"}]], TKI[ Plus[ -2, d], { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_91.1 = OperatorApplyK[e\_91.1]\)], "Input"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_91.2\), "=", RowBox[{ RowBox[{\((d - 2)\), \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], \(\[Nu]\_3\), InterpretationBox[ StyleBox[\(3\^+\), FontWeight->"Bold"], Schiebe[ 3, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["K", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TKI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}], "==", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{\(-2\), \(m\_1\%2\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True]}], "+", \((d - 2 - 2 \[Nu]\_1)\)}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["K", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox[\(d - 2\), "TraditionalForm"], ")"}]], TKI[ Plus[ -2, d], { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_91.2 = OperatorApplyK[e\_91.2]\)], "Input"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_91.3\), "=", RowBox[{ RowBox[{\((d - 2)\), \((d - \[Nu]\_1 - \[Nu]\_2 - \[Nu]\_3)\), InterpretationBox[ SubsuperscriptBox[ StyleBox["K", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TKI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}], "==", RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{\(\[CapitalDelta]\_\(1, 2, 3\)\), "+", RowBox[{\(u\_\(1, 2, 3\)\), InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True]}], "+", RowBox[{\(u\_\(2, 1, 3\)\), InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}], "+", RowBox[{\(u\_\(3, 1, 2\)\), InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}]}], ")"}]}], InterpretationBox[ SubsuperscriptBox[ StyleBox["K", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox[\(d - 2\), "TraditionalForm"], ")"}]], TKI[ Plus[ -2, d], { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_91.3 = OperatorApplyK[e\_91.3]\)], "Input"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_91.4\), "=", RowBox[{ RowBox[{\(\[CapitalDelta]\_\(1, 2, 3\)\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["K", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TKI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}], "==", RowBox[{ RowBox[{"(", RowBox[{ \(\(u\_\(1, 2, 3\)\) \((d - \[Nu]\_1 - 2 \[Nu]\_2)\)\), "+", \(2 \( m\_2\%2\) \((\[Nu]\_1 - \[Nu]\_2)\)\), "+", RowBox[{\(u\_\(3, 1, 2\)\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}], ")"}]}], "+", RowBox[{"2", \(m\_2\%2\), \(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], RowBox[{"(", RowBox[{ InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}], ")"}]}]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["K", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TKI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_91.4 = OperatorApplyK[e\_91.4]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (911)", "Subsection", CellTags->"T1.6.75.1"], Cell[BoxData[ \(h\_911 = s\_91.1 /. \[Nu]\_1 -> \[Nu]\_1 - 1\)], "Input"], Cell[BoxData[ \(f\_911 = MakeFun[h\_911, "\<(911)\>", IFF[\[Nu]\_1 > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]\)], "Input"], Cell["CheckTJIRecursion not applicable.", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (912)", "Subsection", CellTags->"T1.6.76.1"], Cell[BoxData[ \(h\_912 = \(s\_91.2 /. \[Nu]\_2 -> \[Nu]\_2 - 1\) /. \[Nu]\_3 -> \[Nu]\_3 - 1\)], "Input"], Cell[BoxData[ \(f\_912 = MakeFun[h\_912, "\<(912)\>", IFF[\[Nu]\_2 > 1 && \[Nu]\_3 > 1 && MatchQ[d, _Symbol + _Integer?Positive]]]\)], "Input"], Cell["CheckTJIRecursion not applicable.", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (913)", "Subsection", CellTags->"T1.6.77.1"], Cell[BoxData[ \(h\_913 = s\_91.3\)], "Input"], Cell[BoxData[ \(f\_913 = MakeFun[h\_913, "\<(913)\>", IFF[\((n2 === 1\ || \ n3 === 1)\) && MatchQ[d, _Symbol + _Integer?Positive]], n1 :> 1]\)], "Input"], Cell["CheckTJIRecursion not applicable.", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (914)", "Subsection", CellTags->"T1.6.78.1"], Cell[BoxData[ \(h\_914 = s\_91.4 /. \[Nu]\_1 -> \[Nu]\_1 - 1\)], "Input"], Cell[BoxData[ \(f\_914 = MakeFun[h\_914, "\<(914)\>", IFF[\[CapitalDelta]\_\(1, 2, 3\) =!= 0 && \((\[Nu]\_1\ > \ 1\ )\) && MatchQ[d, _Symbol]]]\)], "Input"], Cell["CheckTJIRecursion not applicable.", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Input (92)", "Subsection", CellTags->"T1.6.79.1"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\[CapitalDelta]\_\(1, 2, 3\)\)]], " = Cayley[1,2,3][{m1,m2,m3}]" }], "Text"], Cell[BoxData[ \(\(Cayley[1, 2, 3]\)[{m1, m2, m3}]\)], "Input"], Cell[TextData[Cell[BoxData[ \(TraditionalForm \`\((\ m\_1\%2 == \((m\_2 + m\_3)\)\^2\ )\)\ \[DoubleLongRightArrow]\ \((\ \[CapitalDelta]\_\(1, 2, 3\) == 0\ )\)\)]]], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_92\), "=", RowBox[{ RowBox[{ "2", \(m\_2\), \(m\_3\), \((m\_2 + m\_3)\), \((d - 2 \[Nu]\_1 - 2 \[Nu]\_2 - 2 \[Nu]\_3 - 1)\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["K", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TKI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}], "==", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{\(m\_2\), RowBox[{"(", RowBox[{ RowBox[{ \((d - \[Nu]\_1 - \[Nu]\_2 - 2 \[Nu]\_3 - 1)\), RowBox[{"(", RowBox[{ RowBox[{ InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}], "-", "1"}], ")"}]}], "+", RowBox[{\((\[Nu]\_1 - \[Nu]\_2 + 1)\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}]}], ")"}]}], "+", "\n", "\t\t\t", RowBox[{\(m\_3\), RowBox[{"(", RowBox[{ RowBox[{ \((d - \[Nu]\_1 - 2 \[Nu]\_2 - \[Nu]\_3 - 1)\), RowBox[{"(", RowBox[{ RowBox[{ InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ StyleBox[\(3\^-\), FontWeight->"Bold"], Schiebe[ 3, "-"], Editable->True]}], "-", "1"}], ")"}]}], "+", RowBox[{\((\[Nu]\_1 - \[Nu]\_3 + 1)\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}]}], ")"}]}]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["K", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TKI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_92 = OperatorApplyK[e\_92]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (93)", "Subsection", CellTags->"T1.6.80.1"], Cell[TextData[{ "( ", Cell[BoxData[ \(TraditionalForm \`\(\((m\_1 == 0)\)\ && \ \((m\_2 == m\_3)\)\ \ )\)\ \[DoubleLongRightArrow]\ \((\ \[CapitalDelta]\_\(1, 2, 3\) == 0\ )\)\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_93\), "=", RowBox[{ RowBox[{ "2", \(m\_2\%2\), \((d - 2 \[Nu]\_1 - 2)\), \((d - 2 \[Nu]\_1 - \[Nu]\_2 - \[Nu]\_3 - 1)\), \((d - 2 \[Nu]\_1 - \[Nu]\_2 - \[Nu]\_3)\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["K", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TKI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}], "==", RowBox[{ \((d - 2 \[Nu]\_1 - 2 \[Nu]\_3)\), \((d - 2 \[Nu]\_1 - 2 \[Nu]\_2)\), \((d - \[Nu]\_1 - \[Nu]\_2 - \[Nu]\_3)\), InterpretationBox[ SubsuperscriptBox[ StyleBox["K", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TKI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_93 = OperatorApplyK[e\_93]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (93)", "Subsection", CellTags->"T1.6.81.1"], Cell[BoxData[ \(h\_93 = s\_93 /. \[Nu]\_1 -> \[Nu]\_1 - 1\)], "Input"], Cell[BoxData[ \(f\_93 = MakeFun[h\_93, "\<(93)\>", IFF[\[Nu]\_1 > 1 && m\_2 =!= 0], {m1 :> 0, m3 :> m2}]\)], "Input"], Cell["CheckTJIRecursion not applicable.", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Input (94)", "Subsection", CellTags->"T1.6.82.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_94\), "=", RowBox[{ RowBox[{\(\[CapitalDelta]\_\(1, 2, 6\)\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["B", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TBI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2]}], Editable->True]}], "==", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{\(u\_\(6, 1, 2\)\), RowBox[{"(", RowBox[{ RowBox[{\(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}], "-", "d", "+", \(\[Nu]\_1\), "+", \(2 \[Nu]\_2\)}], ")"}]}], "+", RowBox[{"2", \(m\_2\%2\), RowBox[{"(", RowBox[{ RowBox[{\(\[Nu]\_2\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True]}], "-", "d", "+", \(2 \[Nu]\_1\), "+", \(\[Nu]\_2\)}], ")"}]}]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["B", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TBI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_94 = OperatorApplyB[e\_94]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (94)", "Subsection", CellTags->"T1.6.83.1"], Cell[BoxData[ \(h\_94 = s\_94 /. \[Nu]\_1 -> \[Nu]\_1 - 1\)], "Input"], Cell[BoxData[ \(f\_94 = MakeFun[h\_94, "\<(94)\>", IFF[\[CapitalDelta]\_\(1, 2, 6\) =!= 0 && \[Nu]\_1 > 1]]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (9401)", "Subsection", CellTags->"T1.6.84.1"], Cell[BoxData[ \(n\_9401 = \(s\_94 /. \[CapitalDelta]\_\(1, 2, 6\) -> 0\) /. u\_\(6, 1, 2\) -> 0\)], "Input"], Cell[BoxData[ \(h\_9401 = \(-n\_9401[\([2, 2]\)]\) == n\_9401[\([2, 1]\)]\)], "Input"], Cell[BoxData[ \(f\_9401 = MakeFun[h\_9401, "\<(9401)\>", IFF[\[CapitalDelta]\_\(1, 2, 6\) === 0 && u\_\(6, 1, 2\) === 0 && m2 =!= 0]]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (9402)", "Subsection", CellTags->"T1.6.85.1"], Cell[BoxData[ \(n\_9402 = Interchange[ \(s\_94 /. \[CapitalDelta]\_\(1, 2, 6\) -> 0\) /. u\_\(6, 1, 2\) -> 0, 1 \[LeftRightArrow] 2]\)], "Input"], Cell[BoxData[ \(h\_9402 = \(-n\_9402[\([2, 1]\)]\) == n\_9402[\([2, 2]\)]\)], "Input"], Cell[BoxData[ \(f\_9402 = MakeFun[h\_9402, "\<(9402)\>", IFF[\[CapitalDelta]\_\(1, 2, 6\) === 0 && u\_\(6, 1, 2\) === 0 && m1 =!= 0]]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (95)", "Subsection", CellTags->"T1.6.86.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_95\), "=", RowBox[{ RowBox[{"2", InterpretationBox[\(p\^2\), PP], \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["B", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TBI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2]}], Editable->True]}], "==", RowBox[{ RowBox[{"(", RowBox[{\(u\_\(1, 2, 6\)\), "+", InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True], "-", InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["B", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"]}], RowBox[{"(", FormBox[\(d - 2\), "TraditionalForm"], ")"}]], TBI[ Plus[ -2, d], { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_95 = OperatorApplyB[e\_95]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (95)", "Subsection", CellTags->"T1.6.87.1"], Cell[BoxData[ \(h\_95 = s\_95 /. \[Nu]\_1 -> \[Nu]\_1 - 1\)], "Input"], Cell[BoxData[ \(f\_95 = MakeFun[h\_95, "\<(95)\>", IFF[\[Nu]\_1 > 1\ && \ MatchQ[d, _Symbol + _Integer?Positive]]]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (96)", "Subsection", CellTags->"T1.6.88.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_96\), "=", RowBox[{ RowBox[{"2", InterpretationBox[\(p\^2\), PP], \((d - \[Nu]\_1 - \[Nu]\_2 - 1)\), InterpretationBox[ SubsuperscriptBox[ StyleBox["B", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TBI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2]}], Editable->True]}], "==", RowBox[{ RowBox[{"(", RowBox[{\(\[CapitalDelta]\_\(1, 2, 6\)\), "+", RowBox[{\(u\_\(1, 2, 6\)\), InterpretationBox[ StyleBox[\(1\^-\), FontWeight->"Bold"], Schiebe[ 1, "-"], Editable->True]}], "+", RowBox[{\(u\_\(2, 1, 6\)\), InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True]}]}], ")"}], InterpretationBox[ SubsuperscriptBox[ StyleBox["B", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"]}], RowBox[{"(", FormBox[\(d - 2\), "TraditionalForm"], ")"}]], TBI[ Plus[ -2, d], { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_96 = OperatorApplyB[e\_96]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (96)", "Subsection", CellTags->"T1.6.89.1"], Cell[BoxData[ \(h\_96 = s\_96\)], "Input"], Cell[BoxData[ \(f\_96 = MakeFun[h\_96, "\<(96)\>", IFF[\ MatchQ[d, _Symbol + _Integer\ ?Positive]], n1 :> 1]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (97)", "Subsection", CellTags->"T1.6.90.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_97\), "=", RowBox[{ RowBox[{"2", \(m\_1\%2\), \(\[Nu]\_1\), InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["A", SingleLetterItalics->False, FontWeight->"Bold"], FormBox[\(\[Nu]\_1\), "TraditionalForm"], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TAI[ d, { Subscript[ \[Nu], 1]}], Editable->True]}], "==", RowBox[{\((d - 2 \[Nu]\_1)\), InterpretationBox[ SubsuperscriptBox[ StyleBox["A", SingleLetterItalics->False, FontWeight->"Bold"], FormBox[\(\[Nu]\_1\), "TraditionalForm"], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TAI[ d, { Subscript[ \[Nu], 1]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_97 = OperatorApplyA[e\_97]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (97)", "Subsection", CellTags->"T1.6.91.1"], Cell[BoxData[ \(h\_97 = s\_97 /. \[Nu]\_1 -> \[Nu]\_1 - 1\)], "Input"], Cell[BoxData[ \(f\_97 = MakeFun[h\_97, "\<(97)\>", IFF[\[Nu]\_1 > 1 && \ MatchQ[d, _Symbol\ ]]] \)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (98)", "Subsection", CellTags->"T1.6.92.1"], Cell[TextData[{ "general ", Cell[BoxData[ \(m\_i\%2\)]] }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(e\_98\), "=", RowBox[{ RowBox[{\((d - 2 \[Nu]\_1)\), InterpretationBox[ SubsuperscriptBox[ StyleBox["A", SingleLetterItalics->False, FontWeight->"Bold"], FormBox[\(\[Nu]\_1\), "TraditionalForm"], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TAI[ d, { Subscript[ \[Nu], 1]}], Editable->True]}], "==", RowBox[{\(-2\), \(m\_1\%2\), InterpretationBox[ SubsuperscriptBox[ StyleBox["A", SingleLetterItalics->False, FontWeight->"Bold"], FormBox[\(\[Nu]\_1\), "TraditionalForm"], RowBox[{"(", FormBox[\(d - 2\), "TraditionalForm"], ")"}]], TAI[ Plus[ -2, d], { Subscript[ \[Nu], 1]}], Editable->True]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(s\_98 = OperatorApplyA[e\_98]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (98)", "Subsection", CellTags->"T1.6.93.1"], Cell[BoxData[ \(h\_98 = s\_98\)], "Input"], Cell[BoxData[ \(f\_98 = MakeFun[h\_98, "\<(98)\>", IFF[MatchQ[d, _Symbol\ + _Integer?Positive]]]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (99)", "Subsection", CellTags->"T1.6.94.1"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`m\_1 = M, \ p\^2 = M\^2, m\_2 = \(m\_3 = 0\)\)]]], "Text"], Cell[TextData[{ "Herleitung in three.nb ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ \(-\[Nu]\_1\), " ", \((d - 2\ \[Nu]\_2 - 2\ \[Nu]\_3)\), " ", \((d - \[Nu]\_2 - \[Nu]\_3 - 1)\), " ", SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ StyleBox[ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FontColor->RGBColor[0, 0, 1]], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]]}], "==", RowBox[{ \(\[Nu]\_2\), " ", \((\(-d\) + 2\ \[Nu]\_2 + 2)\), " ", \((\(-2\)\ d + \[Nu]\_1 + 2\ \[Nu]\_2 + 2\ \[Nu]\_3 + 2)\), " ", SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], StyleBox[ FormBox[\(\[Nu]\_2\), "TraditionalForm"], FontColor->RGBColor[0, 0, 1]], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]]}]}], TraditionalForm]]] }], "Text"], Cell[BoxData[ RowBox[{\(e\_99\), "=", RowBox[{ RowBox[{ \(\[Nu]\_1\), " ", \((d - 2\ \[Nu]\_2 - 2\ \[Nu]\_3)\), " ", \((d - \[Nu]\_2 - \[Nu]\_3 - 1)\), " ", InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}], "==", RowBox[{ \(-\[Nu]\_2\), " ", \((\(-d\) + 2\ \[Nu]\_2 + 2)\), " ", \((\(-2\)\ d + \[Nu]\_1 + 2\ \[Nu]\_2 + 2\ \[Nu]\_3 + 2)\), InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}]}]}]], "Input"], Cell[BoxData[ \(s\_99 = OperatorApplyJ[e\_99]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (99)", "Subsection", CellTags->"T1.6.95.1"], Cell[BoxData[ \(h\_99 = s\_99 /. \[Nu]\_1 -> \[Nu]\_1 - 1\)], "Input"], Cell[BoxData[ \(f\_99 = MakeFun[h\_99, "\<(99)\>", IFF[m1^2 === PP && \[Nu]\_1 > 1], {m2 :> 0, m3 :> 0}]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (9912)", "Subsection", CellTags->"T1.6.96.1"], Cell[BoxData[ \(h\_9912 = Interchange[s\_99 /. \[Nu]\_1 -> \[Nu]\_1 - 1, 1 \[LeftRightArrow] 2] \)], "Input"], Cell[BoxData[ \(f\_9912 = MakeFun[h\_9912, "\<(9912)\>", IFF[m2^2 === PP && \[Nu]\_2 > 1], {m1 :> 0, m3 :> 0}]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (9913)", "Subsection", CellTags->"T1.6.97.1"], Cell[BoxData[ \(h\_9913 = Interchange[s\_99 /. \[Nu]\_1 -> \[Nu]\_1 - 1, 1 \[LeftRightArrow] 3] \)], "Input"], Cell[BoxData[ \(f\_9913 = MakeFun[h\_9913, "\<(9913)\>", IFF[m3^2 === PP && \[Nu]\_3 > 1], {m1 :> 0, m2 :> 0}]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (100)", "Subsection", CellTags->"T1.6.98.1"], Cell["Herleitung in three.nb ", "Text"], Cell[TextData[Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ "2", " ", \(m\_2\%2\), " ", \((1 - \[Nu]\_2)\), " ", \(\[Nu]\_2\), " ", InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], StyleBox[ FormBox[\(\[Nu]\_2\), "TraditionalForm"], FontColor->RGBColor[0, 0, 1]], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, { Subscript[ \[Nu], 1], Plus[ 1, Subscript[ \[Nu], 2]], Subscript[ \[Nu], 3]}], Editable->True]}], "==", RowBox[{ RowBox[{\((d - 2\ \[Nu]\_2)\), " ", \((1 - \[Nu]\_2)\), " ", InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}], "-", RowBox[{\(\[Nu]\_1\), " ", \((\(-d\) + 2\ \[Nu]\_1 + 2)\), " ", InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ StyleBox[ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FontColor->RGBColor[0, 0, 1]], StyleBox[ FormBox[\(\[Nu]\_2\), "TraditionalForm"], FontColor->RGBColor[1, 0, 0]], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, { Plus[ 1, Subscript[ \[Nu], 1]], Plus[ -1, Subscript[ \[Nu], 2]], Subscript[ \[Nu], 3]}], Editable->True]}]}]}], TraditionalForm]], "Input"]], "Text"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`m\_1 = 0\)]]], "Text"], Cell[BoxData[ RowBox[{\(e\_100\), "=", RowBox[{ RowBox[{ "2", " ", \(m\_2\%2\), " ", \((1 - \[Nu]\_2)\), " ", \(\[Nu]\_2\), " ", InterpretationBox[ StyleBox[\(2\^+\), FontWeight->"Bold"], Schiebe[ 2, "+"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}], "==", RowBox[{ RowBox[{\((d - 2\ \[Nu]\_2)\), " ", \((1 - \[Nu]\_2)\), " ", InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}], "-", RowBox[{\(\[Nu]\_1\), " ", \((\(-d\) + 2\ \[Nu]\_1 + 2)\), " ", InterpretationBox[ StyleBox[\(1\^+\), FontWeight->"Bold"], Schiebe[ 1, "+"], Editable->True], InterpretationBox[ StyleBox[\(2\^-\), FontWeight->"Bold"], Schiebe[ 2, "-"], Editable->True], InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}]}]}]}]], "Input"], Cell[BoxData[ \(s\_100 = OperatorApplyJ[e\_100]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (100)", "Subsection", CellTags->"T1.6.99.1"], Cell[BoxData[ \(h\_100 = s\_100\)], "Input"], Cell[BoxData[ \(f\_100 = MakeFun[h\_100 /. \[Nu]\_2 -> \[Nu]\_2 - 1, "\<(100)\>", IFF[\[Nu]\_2 > 2 && m2 =!= 0], m1 :> 0]\)], "Input"], Cell[BoxData[ \(CheckTJIRecursion[f\_100]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (1002)", "Subsection", CellTags->"T1.6.100.1"], Cell[BoxData[ \(h\_1002 = Interchange[s\_100, 1 \[LeftRightArrow] 3]\)], "Input"], Cell[BoxData[ \(f\_1002 = MakeFun[h\_1002 /. \[Nu]\_2 -> \[Nu]\_2 - 1, "\<(1002)\>", IFF[\[Nu]\_2 > 2 && m2 =!= 0], m3 :> 0]\)], "Input"], Cell[BoxData[ \(CheckTJIRecursion[f\_1002]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (1003)", "Subsection", CellTags->"T1.6.101.1"], Cell[BoxData[ \(h\_1003 = Interchange[s\_100, 1 \[LeftRightArrow] 3, 1 \[LeftRightArrow] 2]\)], "Input"], Cell[BoxData[ \(f\_1003 = MakeFun[h\_1003 /. \[Nu]\_1 -> \[Nu]\_1 - 1, "\<(1003)\>", IFF[\[Nu]\_1 > 2 && m1 =!= 0], m3 :> 0]\)], "Input"], Cell[BoxData[ \(CheckTJIRecursion[f\_1003]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (1004)", "Subsection", CellTags->"T1.6.102.1"], Cell[BoxData[ \(h\_1004 = Interchange[s\_100, 1 \[LeftRightArrow] 2]\)], "Input"], Cell[BoxData[ \(f\_1004 = MakeFun[h\_1004 /. \[Nu]\_1 -> \[Nu]\_1 - 1, "\<(1004)\>", IFF[\[Nu]\_1 > 2 && m1 =!= 0], m2 :> 0]\)], "Input"], Cell[BoxData[ \(CheckTJIRecursion[f\_1004]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (1005)", "Subsection", CellTags->"T1.6.103.1"], Cell[BoxData[ \(h\_1005 = Interchange[s\_100, 2 \[LeftRightArrow] 3]\)], "Input"], Cell[BoxData[ \(f\_1005 = MakeFun[h\_1005 /. \[Nu]\_3 -> \[Nu]\_3 - 1, "\<(1005)\>", IFF[\[Nu]\_3 > 2 && m3 =!= 0], m1 :> 0]\)], "Input"], Cell[BoxData[ \(CheckTJIRecursion[f\_1005]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (1006)", "Subsection", CellTags->"T1.6.104.1"], Cell[BoxData[ \(h\_1006 = Interchange[s\_100, 2 \[LeftRightArrow] 3, 1 \[LeftRightArrow] 2]\)], "Input"], Cell[BoxData[ \(f\_1006 = MakeFun[h\_1006 /. \[Nu]\_3 -> \[Nu]\_3 - 1, "\<(1006)\>", IFF[\[Nu]\_3 > 2 && m3 =!= 0], m2 :> 0]\)], "Input"], Cell[BoxData[ \(CheckTJIRecursion[f\_1006]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (150)", "Subsection", CellTags->"T1.6.105.1"], Cell[BoxData[ \(TextForm\`\[Nu]\_4 = \(-1\)\)], "Text"], Cell[BoxData[ \(TextForm \`\((q\_2 - p\ )\)\^2 - m\_4\%2 = \ q\_2\%2 - m\_2\%2 - 2 p\ q\_2 + p\^2 + m\_2\%2 - m\_4\%2\)], "Text"], Cell[BoxData[ \(s\_150 = TFI[d, PP, {{n1, m1}, {n2, m2}, {n3, m3}, {\(-1\), m4}, {n5, m5}}] == TFI[d, PP, {{n1, m1}, {n2 - 1, m2}, {n3, m3}, {0, 0}, {n5, m5}}] - 2 TFI[d, PP, {0, 0, 0, 1, 0}, {{n1, m1}, {n2, m2}, {n3, m3}, {0, 0}, {n5, m5}}] + \((PP + m2^2 - m4^2)\) TFI[d, PP, {{n1, m1}, {n2, m2}, {n3, m3}, {0, 0}, {n5, m5}}]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (150)", "Subsection", CellTags->"T1.6.106.1"], Cell[BoxData[ \(h\_150 = s\_150\)], "Input"], Cell[BoxData[ \(f\_150 = MakeFun[h\_150, "\<(150)\>"]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (151)", "Subsection", CellTags->"T1.6.107.1"], Cell[BoxData[ \(TextForm\`\[Nu]\_4 = \(-1\)\)], "Text"], Cell[BoxData[ \(TextForm \`\((q\_2 - p\ )\)\^2 - m\_4\%2 = \ q\_2\%2 - m\_2\%2 - 2 p\ q\_2 + p\^2 + m\_2\%2 - m\_4\%2\)], "Text"], Cell[BoxData[ \(s\_151 = TFI[d, PP, DP, {a, b}, {{n1, m1}, {n2, m2}, {n3, m3}, {\(-1\), m4}, {n5, m5}}] == TFI[d, PP, DP, {a, b}, {{n1, m1}, {n2 - 1, m2}, {n3, m3}, {0, 0}, {n5, m5}}] - 2 TFI[d, PP, DP, {a, b}, {0, 0, 0, 1, 0}, {{n1, m1}, {n2, m2}, {n3, m3}, {0, 0}, {n5, m5}}] + \((PP + m2^2 - m4^2)\) TFI[d, PP, DP, {a, b}, {{n1, m1}, {n2, m2}, {n3, m3}, {0, 0}, {n5, m5}}] \)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (151)", "Subsection", CellTags->"T1.6.108.1"], Cell[BoxData[ \(h\_151 = s\_151\)], "Input"], Cell[BoxData[ \(f\_151 = ReplacePart[MakeFun[h\_151, "\<(151)\>"], {a_, b_}, {1, 1, 4}]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (152)", "Subsection", CellTags->"T1.6.109.1"], Cell[BoxData[ \(TextForm\`\[Nu]\_4 = \(-1\)\)], "Text"], Cell[BoxData[ \(TextForm \`\((q\_2 - p\ )\)\^2 - m\_4\%2 = \ q\_2\%2 - m\_2\%2 - 2 p\ q\_2 + p\^2 + m\_2\%2 - m\_4\%2\)], "Text"], Cell[BoxData[ \(s\_152 = TVI[d, PP, {{n1, m1}, {n2, m2}, {n3, m3}, {\(-1\), m4}}] == TVI[d, PP, {{n1, m1}, {n2 - 1, m2}, {n3, m3}, {0, 0}}] - 2 TFI[d, PP, {0, 0, 0, 1, 0}, {{0, 0}, {n2, m2}, {n3, m3}, {0, 0}, {n1, m1}}] + \((PP + m2^2 - m4^2)\) TVI[d, PP, {{n1, m1}, {n2, m2}, {n3, m3}, {0, 0}}]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (152)", "Subsection", CellTags->"T1.6.110.1"], Cell[BoxData[ \(h\_152 = s\_152\)], "Input"], Cell[BoxData[ \(f\_152 = MakeFun[h\_152, "\<(152)\>"]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (153)", "Subsection", CellTags->"T1.6.111.1"], Cell[BoxData[ \(TextForm\`\[Nu]\_2 = \(-1\)\)], "Text"], Cell[BoxData[ \(s\_153 = TVI[d, PP, {{n1, m1}, {\(-1\), m2}, {n3, m3}, {n4, m4}}] == \n\t\t TFI[d, \ PP, {0, 1, 0, 0, 0}, \ {{0, 0}, {0, 0}, {n3, m3}, {n4, m4}, {n1, m1}}] + m2^2\ TVI[d, \ PP, \ {{n1, m1}, {0, 0}, {n3, m3}, {n4, m4}}]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (153)", "Subsection", CellTags->"T1.6.112.1"], Cell[BoxData[ \(h\_153 = s\_153\)], "Input"], Cell[BoxData[ \(f\_153 = MakeFun[h\_153, "\<(153)\>"]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Input (200)", "Subsection", CellTags->"T1.6.113.1"], Cell["Derivation in TJRspecial.nb", "Text"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`m\_3 = \(m\_2 = m\_1\), \ p\^2 = m\_1\%2\)]]], "Text"], Cell[BoxData[ RowBox[{ RowBox[{\(s\_200\), "=", RowBox[{ RowBox[{ "16", " ", \(m\_1\%2\), " ", \(\[Nu]\_1\), " ", \((d - \[Nu]\_1 - \[Nu]\_2 - \[Nu]\_3)\), " ", InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ StyleBox[ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FontColor->RGBColor[0, 0, 1]], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, { Plus[ 1, Subscript[ \[Nu], 1]], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}], "==", RowBox[{ RowBox[{ \(-\((1 + 3\ d - 3\ \[Nu]\_1 - 4\ \[Nu]\_2)\)\), " ", \(\[Nu]\_3\), " ", InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ StyleBox[ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FontColor->RGBColor[1, 0, 0]], FormBox[\(\[Nu]\_2\), "TraditionalForm"], StyleBox[ FormBox[\(\[Nu]\_3\), "TraditionalForm"], FontColor->RGBColor[0, 0, 1]]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, { Plus[ -1, Subscript[ \[Nu], 1]], Subscript[ \[Nu], 2], Plus[ 1, Subscript[ \[Nu], 3]]}], Editable->True]}], "-", RowBox[{ \(\[Nu]\_2\), " ", \((1 + 3\ d - 3\ \[Nu]\_1 - 4\ \[Nu]\_3)\), " ", InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ StyleBox[ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FontColor->RGBColor[1, 0, 0]], StyleBox[ FormBox[\(\[Nu]\_2\), "TraditionalForm"], FontColor->RGBColor[0, 0, 1]], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, { Plus[ -1, Subscript[ \[Nu], 1]], Plus[ 1, Subscript[ \[Nu], 2]], Subscript[ \[Nu], 3]}], Editable->True]}], "+", RowBox[{ \((\(-1\) + 2\ d - \[Nu]\_1 - 2\ \[Nu]\_2)\), " ", \(\[Nu]\_3\), " ", InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], StyleBox[ FormBox[\(\[Nu]\_2\), "TraditionalForm"], FontColor->RGBColor[1, 0, 0]], StyleBox[ FormBox[\(\[Nu]\_3\), "TraditionalForm"], FontColor->RGBColor[0, 0, 1]]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, { Subscript[ \[Nu], 1], Plus[ -1, Subscript[ \[Nu], 2]], Plus[ 1, Subscript[ \[Nu], 3]]}], Editable->True]}], "-", RowBox[{ \((\(-6\)\ d\^2 + 22\ d\ \[Nu]\_1 - 16\ \[Nu]\_1\%2 - \[Nu]\_2 + 6\ d\ \[Nu]\_2 - 13\ \[Nu]\_1\ \[Nu]\_2 - \[Nu]\_3 + 6\ d\ \[Nu]\_3 - 13\ \[Nu]\_1\ \[Nu]\_3 - 4\ \[Nu]\_2\ \[Nu]\_3)\), " ", InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], FormBox[\(\[Nu]\_2\), "TraditionalForm"], FormBox[\(\[Nu]\_3\), "TraditionalForm"]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, { Subscript[ \[Nu], 1], Subscript[ \[Nu], 2], Subscript[ \[Nu], 3]}], Editable->True]}], "+", RowBox[{ \(\[Nu]\_2\), " ", \((\(-1\) + 2\ d - \[Nu]\_1 - 2\ \[Nu]\_3)\), " ", InterpretationBox[ SubsuperscriptBox[ StyleBox["J", SingleLetterItalics->False, FontWeight->"Bold"], RowBox[{ FormBox[\(\[Nu]\_1\), "TraditionalForm"], StyleBox[ FormBox[\(\[Nu]\_2\), "TraditionalForm"], FontColor->RGBColor[0, 0, 1]], StyleBox[ FormBox[\(\[Nu]\_3\), "TraditionalForm"], FontColor->RGBColor[1, 0, 0]]}], RowBox[{"(", FormBox["d", "TraditionalForm"], ")"}]], TJI[ d, { Subscript[ \[Nu], 1], Plus[ 1, Subscript[ \[Nu], 2]], Plus[ -1, Subscript[ \[Nu], 3]]}], Editable->True]}]}]}]}], ";"}]], "Input"], Cell[BoxData[ \(TextForm \`Due\ to\ sorting\ \ \[Nu]\_1 \[GreaterSlantEqual] \[Nu]\_2 \[GreaterSlantEqual] \[Nu]\_3\ \ by\ TJI\ only\ this\ rule\ is\ \(necessary . \)\)], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (200)", "Subsection", CellTags->"T1.6.114.1"], Cell[BoxData[ \(h\_200 = s\_200 /. \[Nu]\_1 -> \[Nu]\_1 - 1\)], "Input"], Cell[BoxData[ RowBox[{\(f\_200\), "=", RowBox[{ StyleBox["MakeFun", FontColor->RGBColor[1, 0.6, 0.6]], "[", RowBox[{\(h\_200\), ",", "\"\<(200)\>\"", ",", RowBox[{ StyleBox["IFF", FontColor->RGBColor[0.6, 0.4, 1]], "[", \(\[Nu]\_1 > 1 && m1 =!= 0 && PP === m1^2\), "]"}], ",", \({m2 :> m1, m3 :> m1}\)}], "]"}]}]], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (201)", "Subsection", CellTags->"T1.6.115.1"], Cell["\<\ Subscript[f, 201] = HoldForm[TJR[d_, PP_, {{(n1_)?PQ, 0}, {(n2_)?PQ, 0}, {(n3_)?PQ, m3_}}] := (TComment[\"(201)\", TJIC[d, {{n1, 0}, {n2, 0}, {n3, m3}}]]; -(((d - n1 - n2)* (-2 - d + 2*n1 + 2*n2)* (3*d - 2*n1 - 2*n2 - 2*n3)* (-1 - d + n1 + n2 + n3)* TJI[d, PP, {{-1 + n1, 0}, {n2, 0}, {n3, m3}}] )/(2*m3^2*(d - 2*n1)* (-1 + n1)* (2*d - 2*n1 - 2*n2 - n3)* (1 + 2*d - 2*n1 - 2*n2 - n3)))) /; n1 > 1 && m3 =!= 0 && PP === m3^2]\ \>", "Input", Editable->False] }, Closed]], Cell[CellGroupData[{ Cell["MakeFun (202)", "Subsection", CellTags->"T1.6.116.1"], Cell["\<\ Subscript[f, 202] = HoldForm[TJR[d_, PP_, {{(n1_)?PQ, 0}, {(n3_)?PQ, m3_}, {(n2_)?PQ, 0}}] := (TComment[\"(202)\", TJIC[d, {{n1, 0}, {n2, 0}, {n3, m3}}]]; -(((d - n1 - n2)* (-2 - d + 2*n1 + 2*n2)* (3*d - 2*n1 - 2*n2 - 2*n3)* (-1 - d + n1 + n2 + n3)* TJI[d, m3^2, {{-1 + n1, 0}, {n2, 0}, {n3, m3}} ])/(2*m3^2*(d - 2*n1)* (-1 + n1)* (2*d - 2*n1 - 2*n2 - n3)* (1 + 2*d - 2*n1 - 2*n2 - n3)))) /; n1 > 1 && m3 =!= 0 && PP === m3^2]\ \>", "Input", Editable->False] }, Closed]], Cell[CellGroupData[{ Cell[" MakeFun (203)", "Subsection", CellTags->"T1.6.117.1"], Cell[BoxData[ \(Subscript[f, \ 203]\ = HoldForm[\n\t\t\ TJR[d_, \ 0, \ {{\((n1_)\)?PQ, \ 0}, \ {\((n2_)\)?PQ, \ m2_}, \ \n\ \ \ \ {\((n3_)\)?PQ, \ m2_}}]\ := \((\n\t\t\t\t\ TComment["\<(203)\>", \ \n\ \ \ \ \ \ \ \ TJIC[d, 0, \ {{n1, \ 0}, \ {n2, \ m2}, \ {n3, \ m2}}]]; \ \n\t\t \t\t\((\((d\ - \ 2*\((\(-1\)\ + \ n1\ + \ n2)\))\)*\n\ \ \ \ \ \((1\ + \ d\ - \ n1\ - \ n2\ - \ n3)\)*\n\ \ \ \ \ \((d\ - \ 2*\((\(-1\)\ + \ n1\ + \ n3)\))\)*\n\ \ \ \ \ TJR[d, \ 0, \ {{\(-1\)\ + \ n1, \ 0}, \ {n2, \ m2}, \ \n\ \ \ \ \ \ \ {n3, \ m2}}])\)/\n\ \ \ \((2*m2^2*\((d\ - \ 2*n1)\)*\n\ \ \ \ \ \((1\ + \ d\ - \ 2*n1\ - \ n2\ - \ n3)\)*\n\ \ \ \ \ \((2\ + \ d\ - \ 2*n1\ - \ n2\ - \ n3)\))\)\n\t\t\t\n\t \t\t)\)]\)], "Input", Editable->False] }, Closed]], Cell[CellGroupData[{ Cell[" MakeFun (204)", "Subsection", CellTags->"T1.6.118.1"], Cell[BoxData[ \(Subscript[f, \ 204]\ = HoldForm[\n\t\t\ TJR[d_, \ 0, \ {\ {\((n2_)\)?PQ, \ m2_}, \ {\((n1_)\)?PQ, \ 0}, \n\ \ \ \ {\((n3_)\)?PQ, \ m2_}}]\ := \((\n\t\ TComment["\<(204)\>", \ \n\ \ \ \ \ \ \ \ TJIC[d, 0, \ {\ {n2, \ m2}, \ {n1, \ 0}, {n3, \ m2}}]]; \ \n\t \((\((d\ - \ 2*\((\(-1\)\ + \ n1\ + \ n2)\))\)*\n\ \ \ \ \ \((1\ + \ d\ - \ n1\ - \ n2\ - \ n3)\)*\n\ \ \ \ \ \((d\ - \ 2*\((\(-1\)\ + \ n1\ + \ n3)\))\)*\n\ \ \ \ \ TJR[d, \ 0, \ {{\(-1\)\ + \ n1, \ 0}, \ {n2, \ m2}, \ \n\ \ \ \ \ \ \ {n3, \ m2}}])\)/\n\ \ \ \((2*m2^2*\((d\ - \ 2*n1)\)*\n\ \ \ \ \ \((1\ + \ d\ - \ 2*n1\ - \ n2\ - \ n3)\)*\n\ \ \ \ \ \((2\ + \ d\ - \ 2*n1\ - \ n2\ - \ n3)\))\)\n\t\t\t)\)] \)], "Input", Editable->False] }, Closed]], Cell[CellGroupData[{ Cell[" MakeFun (205)", "Subsection", CellTags->"T1.6.119.1"], Cell[BoxData[ \(Subscript[f, \ 205]\ = HoldForm[\n\t\t\ TJR[d_, \ 0, \ {\ {\((n2_)\)?PQ, \ m2_}, \n\ \ \ \ {\((n3_)\)?PQ, \ m2_}, \ {\((n1_)\)?PQ, \ 0}}]\ := \((\n\t\ TComment["\<(205)\>", \ \n\ \ \ \ \ \ \ \ TJIC[d, 0, \ {\ {n2, \ m2}, {n3, \ m2}, \ {n1, \ 0}}]]; \ \n \((\((d\ - \ 2*\((\(-1\)\ + \ n1\ + \ n2)\))\)*\n\ \ \ \ \ \((1\ + \ d\ - \ n1\ - \ n2\ - \ n3)\)*\n\ \ \ \ \ \((d\ - \ 2*\((\(-1\)\ + \ n1\ + \ n3)\))\)*\n\ \ \ \ \ TJR[d, \ 0, \ {{\(-1\)\ + \ n1, \ 0}, \ {n2, \ m2}, \ \n\ \ \ \ \ \ \ {n3, \ m2}}])\)/\n\ \ \ \((2*m2^2*\((d\ - \ 2*n1)\)*\n\ \ \ \ \ \((1\ + \ d\ - \ 2*n1\ - \ n2\ - \ n3)\)*\n\ \ \ \ \ \((2\ + \ d\ - \ 2*n1\ - \ n2\ - \ n3)\))\)\n\t\t\t)\)] \)], "Input", Editable->False] }, Closed]], Cell[CellGroupData[{ Cell["Input (1xxxx)", "Subsection", CellTags->"T1.6.120.1"], Cell["\<\ If[MatchQ[$RankLimit, {_Integer?NonNegative, _Integer?NonNegative}], $TarasovTdeltaplimit = $RankLimit[[1]]; ($TarasovTplimit = $RankLimit[[2]]; ), $TarasovTdeltaplimit = 2; $TarasovTplimit = 2]; \ \>", "Input"], Cell[BoxData[ RowBox[{"tarti", "=", RowBox[{"Timing", "[", RowBox[{"Do", "[", RowBox[{ RowBox[{"If", "[", RowBox[{\(0 < a + b + r + es\), ",", RowBox[{\(WriteString["\", {a, b, r, es}]\), ";", RowBox[{"Set", "@@", RowBox[{"{", RowBox[{ \(s\_\(10\^4 + 1000\ a + 100\ b + 10\ r + es\)\), ",", RowBox[{ RowBox[{ RowBox[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], "[", RowBox[{"d", ",", InterpretationBox[\(p\^2\), PP], ",", "DP", ",", \({a, b}\), ",", \({0, 0, r, es, 0}\), ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", InterpretationBox[\(m\_1\), m1]}], "}"}], ",", RowBox[{"{", RowBox[{"n2", ",", InterpretationBox[\(m\_2\), m2]}], "}"}], ",", RowBox[{"{", RowBox[{"n3", ",", InterpretationBox[\(m\_3\), m3]}], "}"}], ",", RowBox[{"{", RowBox[{"n4", ",", InterpretationBox[\(m\_4\), m4]}], "}"}], ",", RowBox[{"{", RowBox[{"n5", ",", InterpretationBox[\(m\_5\), m5]}], "}"}]}], "}"}]}], "]"}], "==", RowBox[{"ApplyTarasovT", "[", RowBox[{ RowBox[{"TarasovT", "[", RowBox[{ "a", ",", "b", ",", "r", ",", "es", ",", InterpretationBox[\(p\^2\), PP], ",", "DP"}], "]"}], ",", RowBox[{"STLI", "[", RowBox[{"d", ",", InterpretationBox[\(p\^2\), PP], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"n1", ",", InterpretationBox[\(m\_1\), m1]}], "}"}], ",", RowBox[{"{", RowBox[{"n2", ",", InterpretationBox[\(m\_2\), m2]}], "}"}], ",", RowBox[{"{", RowBox[{"n3", ",", InterpretationBox[\(m\_3\), m3]}], "}"}], ",", RowBox[{"{", RowBox[{"n4", ",", InterpretationBox[\(m\_4\), m4]}], "}"}], ",", RowBox[{"{", RowBox[{"n5", ",", InterpretationBox[\(m\_5\), m5]}], "}"}]}], "}"}]}], "]"}]}], "]"}]}], "/.", RowBox[{"STLI", "\[Rule]", StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]]}]}]}], "}"}]}]}]}], "]"}], ",", \({a, 0, $TarasovTdeltaplimit}\), ",", \({b, 0, $TarasovTdeltaplimit - a}\), ",", \({r, 0, $TarasovTplimit}\), ",", \({es, 0, $TarasovTplimit - r}\)}], "]"}], "]"}]}]], "Input"], Cell[BoxData[ \(Share[]\)], "Input"], Cell[BoxData[ \(matarti = Timing[Do[ If[0 < ia + ib + ir + es, WriteString["\", {ia, ib, ir, es}]; tt[ia, ib, ir, es] = Set[f\_\(10\^4 + 1000\ ia + 100\ ib + 10\ ir + es\), MakeFun[s\_\(10\^4 + 1000\ ia + 100\ ib + 10\ ir + es\), "\<(1\>"<>ToString[ia]<>ToString[ib]<>ToString[ir]<> ToString[es]<>"\<)\>"] /. PQ :> PNQ]], {ia, 0, \ $TarasovTdeltaplimit}, {ib, 0, $TarasovTdeltaplimit - ia}, {ir, 0, \ \ $TarasovTplimit}, {es, 0, $TarasovTplimit - ir}]]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["five -> four", "Subsection", CellTags->"T1.6.121.1"], Cell[BoxData[ \(TFI[d_, \ PP_ /; Head[PP] =!= List, {\ {0, \ m1_}, \ {n2_, \ m2_}, \ \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {n3_, \ m3_}, \ {n4_, \ m4_}, \ \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {n5_, \ m5_}\ }]\ := \ \n TVI[d, PP, \ {{n5, m5}, \ {n2, m2}, \ {n3, m3}, \ {n4, m4}}]\)], "Input"], Cell[BoxData[ \(TFI[d_, \ \ PP_ /; Head[PP] =!= List, {\ {\((n2_)\), \ m2_}, {0, \ m1_}, \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\((n4_)\), \ m4_}, \ {\((n3_)\), \ m3_}, \ \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\((n5_)\), \ m5_}\ }] \ := \ \n TVI[d, PP, \ {{n5, m5}, \ {n2, m2}, \ {n3, m3}, \ {n4, m4}}]\)], "Input"], Cell[BoxData[ \(TFI[d_, \ \ \ PP_ /; Head[PP] =!= List, {\ {\((n3_)\), \ m3_}, \ {\((n4_)\), \ m4_}, \n\t\t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {0, \ m1_}, \ {\((n2_)\), \ m2_}, \ \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\((n5_)\), \ m5_}\ }] \ := \ \n TVI[d, PP, \ {{n5, m5}, \ {n2, m2}, \ {n3, m3}, \ {n4, m4}}]\)], "Input"], Cell[BoxData[ \(TFI[d_, \ \ \ PP_ /; Head[PP] =!= List, {\ {\((n4_)\), \ m4_}, {\((n3_)\), \ m3_}, \n\t\t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\((n2_)\), \ m2_}, \ {0, \ m1_}, \ \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\((n5_)\), \ m5_}\ }]\ := \ \n TVI[d, PP, \ {{n5, m5}, \ {n2, m2}, \ {n3, m3}, \ {n4, m4}}]\)], "Input"], Cell["\<\ TFI[d_, PP_/;Head[PP]=!=List,{{(n1_), m1_}, {(n2_), m2_}, {(n3_), m3_}, {(n4_), m4_}, {0, m5_}}] := TBI[d, PP, {{n1, m1}, {n3, m3}}]* TBI[d, PP, {{n2, m2}, {n4, m4}}] \ \>", "Input"] }, Closed]], Cell[CellGroupData[{ Cell["four -> three", "Subsection", CellTags->"T1.6.122.1"], Cell[BoxData[ \(TVI[d_, \ PP_, {\ {0, \ m1_}, \ {n2_, \ m2_}, \ \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {n3_, \ m3_}, \ {n4_, \ m4_}\ }] \ := \ \nTAI[d, 0, {{n3, m3}}]\ TBI[d, PP, {{n2, m2}, {n4, m4}}]\)], "Input"], Cell[BoxData[ \(TVI[d_, \ PP_, {\ {n1_, \ m1_}, \ {n2_, \ m2_}, \ \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {0, \ m3_}, \ {n4_, \ m4_}\ }] \ := \ \nTAI[d, 0, {{n1, m1}}]\ TBI[d, PP, {{n2, m2}, {n4, m4}}]\)], "Input"], Cell["\<\ TVI[d_, PP_, {{n1_, m1_}, {0, m2_}, {n3_, m3_}, {n4_, m4_}}] := TJI[d, 0, {{n1, m1}, {n3, m3}, {n4, m4}}]\ \>", "Input"], Cell[BoxData[ \(TVI[d_, \ PP_, {\ {n1_, \ m1_}, \ {n2_, \ m2_}, \ \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {n3_, \ m3_}, \ {0, \ m4_}\ }] \ := \ \nTJI[d, PP, \ {{n2, m2}, {n1, m1}, {n3, m3}\ }]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["three -> two", "Subsection", CellTags->"T1.6.123.1"], Cell[BoxData[ \(TJI[d_, \ PP_, {\ {0, \ m1_}, \ {\((n2_)\), \ m2_}, \ {\((n3_)\), \ m3_}\ }] \ := \ \nTAI[d, 0, {{n2, m2}}]\ \ TAI[d, 0, {{n3, m3}}]\)], "Input"], Cell[BoxData[ \(TJI[d_, \ PP_, {\ {\((n1_)\), \ m1_}, \ {0, \ m2_}, \ {\((n3_)\), \ m3_}\ }] \ := \ \nTAI[d, 0, {{n1, m1}}]\ \ TAI[d, 0, {{n3, m3}}]\)], "Input"], Cell[BoxData[ \(TJI[d_, \ PP_, {\ {\((n1_)\), \ m1_}, \ {\((n2_)\), \ m2_}, \ {0, \ m3_}\ }] \ := \ \nTAI[d, 0, {{n1, m1}}]\ \ TAI[d, 0, {{n2, m2}}]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["two -> one", "Subsection", CellTags->"T1.6.124.1"], Cell[BoxData[ \(\(TBI[d_, \ PP_, {\ {0, \ m1_}, \ {\((n2_)\), \ m2_}\ }]\ := \ \n TAI[d, 0, {{n2, m2}}]\ \)\)], "Input"], Cell[BoxData[ \(\(TBI[d_, \ PP_, {\ {\((n1_)\), \ m1_}, \ {0, \ m2_}\ }]\ := \ \n TAI[d, 0, {{n1, m1}}]\ \)\)], "Input"], Cell[BoxData[ \(\(TAI[d_, {{n_Integer, m_}}] := TAI[d, 0, {{n, m}}]; \)\)], "Input"], Cell[BoxData[ \(\(TAI[d_, {n_Integer, m_}] := TAI[d, 0, {{n, m}}]; \)\)], "Input"], Cell[BoxData[ \(\(TAI[d_, 0, {n_Integer, m_}] := TAI[d, 0, {{n, m}}]; \)\)], "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["TarcerRecurse and TFIRecurse", "Section", CellDingbat->"\[FilledSmallCircle]", CellTags->"T1.7.1"], Cell[CellGroupData[{ Cell["TFIRecurse", "Subsection", CellTags->"T1.7.1.1"], Cell["This cancels scalar products.", "Text"], Cell[BoxData[{\($TLRComment = False; \), \(TLRComment[s_String] := Print[s] /; $TLRComment === True; \), RowBox[{ RowBox[{\(TFIRecurse[z_]\), ":=", RowBox[{ RowBox[{ RowBox[{"z", "/.", RowBox[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], "\[Rule]", "TLR"}]}], "//.", "TLRules"}], "/.", RowBox[{"TLR", "\[Rule]", StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]]}]}]}], ";"}]}], "Input"], Cell[BoxData[{ \(\(ExpandMaybe[z_] := z; \)\), \(\(fN[li_List] := \(fN[li] = li /. {0, _} \[RuleDelayed] {0, 0}\); \)\)}], "Input"], Cell[BoxData[ RowBox[{ RowBox[{\(tlrule[1]\), "=", RowBox[{\(TLR[d_, pp_, {0, 0, 0, 0, 0}, pr_]\), "\[RuleDelayed]", RowBox[{"(", RowBox[{\(NoTLRComment["\"]\), ";", RowBox[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], "[", \(d, pp, pr /. {0, _} \[RuleDelayed] {0, 0}\), "]"}]}], ")"}]}]}], ";"}]], "Input"], Cell["(* q1^2 *)", "Text"], Cell[BoxData[ \(\(tlrule[2] = TLR[dpp__, {v_?PQ, w_, x_, y_, z_}, {{n1_?PQ, m1_}, nm2_, nm3_, nm4_, nm5_}] \[RuleDelayed] \((TLRComment["\"]; ExpandMaybe[ If[v \[LessEqual] n1, If[m1 === 0, TLR[dpp, {0, w, x, y, z}, {{n1 - v, 0}, nm2, nm3, nm4, nm5}], \[Sum]\+\(i = 0\)\%v Binomial[v, i]\ TLR[dpp, \ {0, w, x, y, z}, {fN[{n1 - i, m1}], nm2, nm3, nm4, nm5}]\ \((m1\^2)\)\^\(v - i\)], If[m1 === 0, TLR[dpp, {v - n1, w, x, y, z}, {{0, 0}, nm2, nm3, nm4, nm5}], \[Sum]\+\(i = 0\)\%n1 Binomial[n1, i]\ TLR[dpp, {v - n1, w, x, y, z}, {fN[{n1 - i, m1}], nm2, nm3, nm4, nm5}]\ \((m1\^2)\)\^\(n1 - i\)]]])\); \)\)], "Input"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`q\_2\%2\)]]], "Text"], Cell[BoxData[ \(\(tlrule[3] = TLR[dpp__, {v_, w_?PQ, x_, y_, z_}, {nm1_, {n2_?PQ, m2_}, nm3_, nm4_, nm5_}] \[RuleDelayed] \((TLRComment["\"]; ExpandMaybe[ If[w \[LessEqual] n2, If[m2 === 0, TLR[dpp, {v, 0, x, y, z}, {nm1, {n2 - w, 0}, nm3, nm4, nm5}], \[Sum]\+\(i = 0\)\%w Binomial[w, i]\ TLR[dpp, {v, 0, x, y, z}, {nm1, fN[{n2 - i, m2}], nm3, nm4, nm5}]\ \((m2\^2)\)\^\(w - i\)], If[m2 === 0, TLR[dpp, {v, w - n2, x, y, z}, {nm1, {0, 0}, nm3, nm4, nm5}], \[Sum]\+\(i = 0\)\%n2 Binomial[n2, i]\ TLR[dpp, {v, w - n2, x, y, z}, {nm1, fN[{n2 - i, m2}], nm3, nm4, nm5}]\ \((m2\^2)\)\^\(n2 - i\)]]])\); \)\)], "Input"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`p\[CenterDot]q\_1\)]]], "Text"], Cell[BoxData[ \(\(tlrule[4] = TLR[dpp__, {v_, w_, x_?PQ, y_, z_}, {{n1_?PQ, m1_}, nm2_, {n3_?PQ, m3_}, nm4_, nm5_}] \[RuleDelayed] \((TLRComment["\"]; ExpandMaybe[ 1\/2\ TLR[ dpp, {v + 1, w, x - 1, y, z}, {{n1, m1}, nm2, {n3, m3}, nm4, nm5}] - 1\/2\ TLR[ dpp, {v, w, x - 1, y, z}, {{n1, m1}, nm2, fN[{n3 - 1, m3}], nm4, nm5}] + 1\/2\ \(({dpp}\[LeftDoubleBracket]2\[RightDoubleBracket] - m3\^2)\)\ TLR[dpp, {v, w, x - 1, y, z}, {{n1, m1}, nm2, {n3, m3}, nm4, nm5}]])\); \)\)], "Input"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`p\[CenterDot]q\_2\)]]], "Text"], Cell[BoxData[ \(\(tlrule[5] = TLR[dpp__, {v_, w_, x_, y_?PQ, z_}, {{n1_, m1_}, {n2_?PQ, m2_}, nm3_, {n4_?PQ, m4_}, nm5_}] \[RuleDelayed] \((TLRComment["\"]; ExpandMaybe[ 1\/2\ TLR[ dpp, {v, w + 1, x, y - 1, z}, {{n1, m1}, {n2, m2}, nm3, {n4, m4}, nm5}] - 1\/2\ TLR[ dpp, {v, w, x, y - 1, z}, {{n1, m1}, {n2, m2}, nm3, fN[{n4 - 1, m4}], nm5}] + 1\/2\ \(({dpp}\[LeftDoubleBracket]2\[RightDoubleBracket] - m4\^2)\)\ TLR[dpp, {v, w, x, y - 1, z}, {{n1, m1}, {n2, m2}, nm3, {n4, m4}, nm5}]])\); \)\)], "Input"], Cell[TextData[Cell[BoxData[ \(TraditionalForm\`q\_1\[CenterDot]q\_2\)]]], "Text"], Cell[BoxData[ \(\(tlrule[6] = TLR[dpp__, {v_, w_, x_, y_, z_?PQ}, {{n1_, m1_}, {n2_, m2_}, nm3_, nm4_, {n5_?PQ, m5_}}] \[RuleDelayed] \((TLRComment["\"]; ExpandMaybe[ 1\/2\ TLR[ dpp, {v + 1, w, x, y, z - 1}, {{n1, m1}, {n2, m2}, nm3, nm4, {n5, m5}}] - 1\/2\ TLR[ dpp, {v, w, x, y, z - 1}, {{n1, m1}, {n2, m2}, nm3, nm4, fN[{n5 - 1, m5}]}] + 1\/2\ TLR[ dpp, {v, w + 1, x, y, z - 1}, {{n1, m1}, {n2, m2}, nm3, nm4, {n5, m5}}] - 1\/2\ m5\^2\ TLR[dpp, {v, w, x, y, z - 1}, {{n1, m1}, {n2, m2}, nm3, nm4, {n5, m5}}]])\); \)\)], "Input"], Cell["(* q1.q1 --> q1.p *)", "Text"], Cell[BoxData[ \(\(tlrule[7] = TLR[d_, pp_, dp___, {v_?PQ, w_, x_, y_, z_}, {{0, _}, nm2_, {n3_?PQ, m3_}, nm4_, nm5_}] \[RuleDelayed] \((TLRComment["\"]; ExpandMaybe[ TLR[d, pp, dp, {v - 1, w, x, y, z}, {{0, 0}, nm2, fN[{n3 - 1, m3}], nm4, nm5}] + 2\ TLR[d, pp, dp, {v - 1, w, x + 1, y, z}, {{0, 0}, nm2, {n3, m3}, nm4, nm5}] - \((pp - m3\^2)\)\ TLR[d, pp, dp, {v - 1, w, x, y, z}, {{0, 0}, nm2, {n3, m3}, nm4, nm5}]])\); \)\)], "Input"], Cell["(* q2.q2 --> q2.p *)", "Text"], Cell[BoxData[ \(\(tlrule[8] = TLR[d_, pp_, dp___, {v_, w_?PQ, x_, y_, z_}, {nm1_, {0, _}, nm3_, {n4_?PQ, m4_}, nm5_}] \[RuleDelayed] \((TLRComment["\"]; ExpandMaybe[ TLR[d, pp, dp, {v, w - 1, x, y, z}, {nm1, {0, 0}, nm3, fN[{n4 - 1, m4}], nm5}] + 2\ TLR[d, pp, dp, {v, w - 1, x, y + 1, z}, {nm1, {0, 0}, nm3, {n4, m4}, nm5}] - \((pp - m4\^2)\)\ TLR[d, pp, dp, {v, w - 1, x, y, z}, {nm1, {0, 0}, nm3, {n4, m4}, nm5}]])\); \)\)], "Input"], Cell["(* eq. (3) - (5) *)", "Text"], Cell[BoxData[ \(\(tlrule[9] = TLR[d_, pp_, {v_, w_, x_, y_, z_?PQ}, {nm1_, nm2_, nm3_, nm4_, {0, _}}] \[RuleDelayed] \((TLRComment["\"]; ExpandMaybe[ \[Sum]\+\(k = 0\)\%\(Floor[z\/2]\)\(\[Sum]\+\(i = 0\)\%k \(\[Sum]\+\(j = 0\)\%k \((Gamma[k + 1\/2]\ Gamma[d\/2 - 1\/2]\ Binomial[z, 2\ k]\ Binomial[k, i]\ Binomial[k, j]\ \((\(-1\))\)\^\(i + j\)\ pp\^\(i + j - z\)\ TLR[d, pp, {v + i, w + j, x + z - 2\ i, y + z - 2\ j, 0}, { nm1, nm2, nm3, nm4, {0, 0}}])\)/ \((Gamma[1\/2]\ Gamma[k + d\/2 - 1\/2])\)\)\)])\); \)\)], "Input"], Cell["\<\ tlrule[10] = (* (9) and (10) *) TLR[d_, pp_, {v_,w_,x_?PQ,y_?PQ,z_}, {{n1_?PQ,m1_},{n2_?PQ,m2_}, {0,_},{0,_},nm5_}] :> ( TLRComment[\"tlrule10\"]; 0 /; OddQ[x+y] );\ \>", "Input"], Cell["\<\ Bug in tlrule[11] and tlrule[12] fixed on Feb. 26th 1998 by \ R.Scharf with thanks to York Schroeder for locating the bug.\ \>", "Text"], Cell["\<\ tlrule[11] = TLR[d_, pp_, {v_,w_,x_?PQ,y_?PQ,z_}, {nm1_,nm2_,{0,_},{0,_},nm5_}] :> ( TLRComment[\"tlrule11\"]; ExpandMaybe[ pp/(d+x+y-2)( (x-1) TLR[d, pp, {v+1,w,x-2,y,z}, {{n1,m1},{n2,m2},{0,0},{0,0},nm5}] + y TLR[d, pp, {v,w,x-1,y-1,z+1}, {nm1,nm2,{0,0},{0,0},nm5}] ) ] /; EvenQ[x+y] && x > 1 );\ \>", "Input"], Cell["\<\ tlrule[12] = TLR[d_, pp_, {v_,w_,x_?PQ,y_?PQ,z_}, {nm1_,nm2_,{0,_},{0,_},nm5_}] :> ( TLRComment[\"tlrule12\"]; ExpandMaybe[ pp/(d+x+y-2)( (y-1) TLR[d, pp, {v,w+1,x,y-2,z}, {{n1,m1},{n2,m2},{0,0},{0,0},nm5}] + x TLR[d, pp, {v,w,x-1,y-1,z+1}, {nm1,nm2,{0,0},{0,0},nm5}] ) ] /; EvenQ[x+y] && y > 1 );\ \>", "Input"], Cell["(*symm. 1 <-> 3 && 2 <-> 4 *)", "Text"], Cell[BoxData[ \(\(tlrule[13] = TLR[d_, pp_, {0, 0, 0, y_?PQ, 0}, {nm1_, {0, 0}, nm3_, {n4_?PQ, m4_}, nm5_}] \[RuleDelayed] \((TLRComment["\"]; \[Sum]\+\(i = 0\)\%y Binomial[y, i]\ pp\^\(y - i\)\ \((\(-1\))\)\^i\ TLR[d, pp, {0, 0, 0, i, 0}, {nm3, {n4, m4}, nm1, {0, 0}, nm5}]) \); \)\)], "Input"], Cell["(*symm. 1 <-> 3 && 2 <-> 4 *)", "Text"], Cell[BoxData[ \(\(tlrule[14] = TLR[d_, pp_, {0, 0, x_?PQ, 0, 0}, {{0, 0}, nm2_, {n3_?PQ, m3_}, nm4_, nm5_}] \[RuleDelayed] \((TLRComment["\"]; \[Sum]\+\(i = 0\)\%x Binomial[x, i]\ pp\^\(x - i\)\ \((\(-1\))\)\^i\ TLR[d, pp, {0, 0, i, 0, 0}, {{n3, m3}, nm4, {0, 0}, nm2, nm5}]) \); \)\)], "Input"], Cell["(* 0's *)", "Text"], Cell[BoxData[ \(\(tlrule[15] = TLR[d_, pp_, {v_, w_, x_, y_, z_}, {{n1_, 0}, {n2_, 0}, {0, _}, {0, _}, {0, _}}] \[RuleDelayed] \((TLRComment["\"]; 0)\); \)\)], "Input"], Cell[BoxData[ \(\(tlrule[16] = TLR[d_, pp_, {0, 0, x_?PQ, y_?PQ, 0}, {{n1_, _}, {n2_, _}, {0, _}, {0, _}, {0, _}}] \[RuleDelayed] \((TLRComment["\"]; 0 /; OddQ[x] || OddQ[y])\); \)\)], "Input"], Cell[BoxData[ \(\(tlrule[17] = TLR[d_, pp_, {a_?PQ, b_, 0, de_, 0}, {{0, _}, {n2_, m2_}, {0, _}, {n4_, m4_}, {n5_, m5_}}] \[RuleDelayed] \((TLRComment["\"]; \[Sum]\+\(i = 0\)\%a \(\[Sum]\+\(j = 0\)\%i Binomial[a, i]\ Binomial[i, j]\ \((1 + \((\(-1\))\)\^j)\)\ 2\^\(j - 1\)\ TLR[d, pp, {a - i, i - j, 0, 0, j}, {{n5, m5}, {n2, m2}, {0, 0}, {n4, m4}, {0, 0}}]\))\); \)\)], "Input"], Cell[BoxData[ \(\(tlrule[18] = TLR[d_, pp_, dp_, {a_?PNQ, b_?PNQ}, {1, 0, 0, 0, 0}, {{0, 0}, {n2_, m2_}, {n3_, m3_}, {n4_, m4_}, {n5_, m5_}}] \[RuleDelayed] \((TLRComment["\"]; \[Sum]\+\(i = 0\)\%a \(\[Sum]\+\(j = 0\)\%b Binomial[a, i]\ Binomial[b, j]\ \((\((pp + m3\^2)\)\ TLR[d, pp, dp, {i, j}, {{n3, m3}, {n4, m4}, {0, 0}, {n2, m2}, {n5, m5}}] + TLR[d, pp, dp, {i, j}, {{n3 - 1, m3}, {n4, m4}, {0, 0}, {n2, m2}, {n5, m5}}] - 2\ TLR[d, pp, dp, {i, j}, {0, 0, 1, 0, 0}, {{n3, m3}, {n4, m4}, {0, 0}, {n2, m2}, {n5, m5}}])\)\ \((\(-1\))\)\^\(i + j\)\ dp\^\(a + b - i - j\)\))\); \)\)], "Input"], Cell[BoxData[ \(\(tlrule[19] = TLR[d_, pp_, dp_, {a_?PNQ, b_?PNQ}, {0, 1, 0, 0, 0}, {{n1_, m1_}, {0, 0}, {n3_, m3_}, {n4_, m4_}, {n5_, m5_}}] \[RuleDelayed] \((TLRComment["\"]; \[Sum]\+\(i = 0\)\%a \(\[Sum]\+\(j = 0\)\%b Binomial[a, i]\ Binomial[b, j]\ \((\((pp + m4\^2)\)\ TLR[d, pp, dp, {i, j}, {{n3, m3}, {n4, m4}, {n1, m1}, {0, 0}, {n5, m5}}] + TLR[d, pp, dp, {i, j}, {{n3, m3}, {n4 - 1, m4}, {n1, m1}, {0, 0}, {n5, m5}}] - 2\ TLR[d, pp, dp, {i, j}, {0, 0, 0, 1, 0}, {{n3, m3}, {n4, m4}, {n1, m1}, {0, 0}, {n5, m5}}])\)\ \((\(-1\))\)\^\(i + j\)\ dp\^\(a + b - i - j\)\))\); \)\)], "Input"], Cell["(* q1.q1 --> q1.p *)", "Text"], Cell[BoxData[ \(\(tlrule[20] = TLR[d_, pp_, {v_?PQ, w_, x_, y_, 0}, {{0, _}, nm2_, {0, _}, nm4_, {n5_?PQ, m5_}}] \[RuleDelayed] \((TLRComment["\"]; \[Sum]\+\(j = 0\)\%x \(\[Sum]\+\(i = 0\)\%v \(\[Sum]\+\(r = 0\)\%i Binomial[i, r]\ Binomial[v, i]\ Binomial[x, j]\ 2\^r\ TLR[d, pp, {v - i, \(-r\) + i + w, j, x - j + y, r}, {{n5, m5}, nm2, 0, nm4, 0}]\)\))\); \)\)], "Input"], Cell[BoxData[ \(\(tlrule[21] = TLR[d_, pp_, {v_, w_?PQ, x_, y_, 0}, {nm1_, {0, _}, nm3_, {0, _}, nm5_}] \[RuleDelayed] \((TLRComment["\"]; TLR[d, pp, {w, v, y, x, 0}, {{0, 0}, nm1, {0, 0}, nm3, nm5}])\); \)\)], "Input"], Cell["\<\ TLRules = Array[tlrule, 21]; TLR[__, { {_,_},{0,_},{_,_},{0,_},{_,0} }] := 0 ; TLR[__, { {0,_},{_,_},{0,_},{_,_},{_,0} }] := 0 ; TLR[__, { {0,_},{_,_},{_,0},{_,_},{0,_} }] := 0 ; TLR[__, { {_,0},{_,_},{0,_},{_,_},{0,_} }] := 0 ; TLR[__, { {_,_},{_,0},{_,_},{0,_},{0,_} }] := 0 ; TLR[__, { {_,_},{0,_},{_,_},{_,0},{0,_} }] := 0 ; SetAttributes[seeetDelayed,HoldAll]; seeetDelayed[TLR[a__],b_]:= Apply[SetDelayed,{TLR[a],b}] lis1=Permutations[{ {0,_},{0,_},{0,_},{_,_},{_,0} }]; lis2=Table[TLR[__, lis1[[i]]]:>0, {i, \ Length[lis1]}]/.RuleDelayed->seeetDelayed; Clear[lis1,lis2];\ \>", "Input"] }, Closed]], Cell[CellGroupData[{ Cell["T*IS", "Subsection", CellTags->"T1.7.2.1"], Cell["\<\ These functions below are never used. They can serve as tests.\ \>", "Text"], Cell[BoxData[ \(\(TJIS[d_, Power[M_, \ 2], \ {{\[Alpha]_, 0}, {\[Beta]_, 0}, {\[Gamma]_, 0}}] := \(SMu\^2\) \((\(\((\(-1\))\)\^\(\[Alpha] + \[Beta] + \[Gamma] + 1\)\/\(( \(-\ M\^2\))\)\^\(\[Alpha] + \[Beta] + \[Gamma] - 4\)\) Exp[\(-I\)\ Pi\ \((d - 4)\)]\ \(Gamma[\[Alpha] + \[Beta] + \[Gamma] - d]\/Gamma[ \(3\/2\) d - \[Alpha] - \[Beta] - \[Gamma]]\) \(Gamma[d\/2 - \[Alpha]]\/Gamma[\[Alpha]]\) \(Gamma[d\/2 - \[Beta]]\/Gamma[\[Beta]]\) Gamma[d\/2 - \[Gamma]]\/Gamma[\[Gamma]])\)\n\)\)], "Input"], Cell[BoxData[ \(TJIS[d_, Power[M_, \ 2], \ {{\[Beta]_, 0}, {\[Gamma]_, 0}, {\[Alpha]_, M_}}] := \n\t TJIS[d, M^2, {{\[Alpha], M}, {\[Beta], 0}, {\[Gamma], 0}}]\)], "Input"], Cell[BoxData[ \(TJIS[d_, Power[M_, \ 2], \ {{\[Beta]_, 0}, {\[Alpha]_, M_}, {\[Gamma]_, 0}}] := \n\t TJIS[d, M^2, {{\[Alpha], M}, {\[Beta], 0}, {\[Gamma], 0}}]\)], "Input"], Cell[BoxData[ \(TJIS[d_, Power[M_, \ 2], \ {{\[Alpha]_, M_}, {\[Beta]_, 0}, {\[Gamma]_, 0}}] := \n \(SMu\^2\/\((M\^2)\)\^\(\[Alpha] + \[Beta] + \[Gamma] - 4\)\) \(\((\(-1\))\)\^\(\[Alpha] + \[Beta] + \[Gamma] + 1\)\) \(Gamma[\[Alpha] + \[Beta] + \[Gamma] - d]\/\(Gamma[\[Alpha]] Gamma[\[Beta]] Gamma[\[Gamma]]\)\) \(\(Gamma[d\/2 - \[Gamma]] Gamma[d\/2 - \[Beta]]\)\/Gamma[ d - \[Beta] - \[Gamma]]\) \(Gamma[\[Beta] + \[Gamma] - d\/2] Gamma[2\ d - \[Alpha] - 2 \[Beta] - 2 \[Gamma]]\)\/Gamma[ \(3 d\)\/2 - \[Alpha] - \[Beta] - \[Gamma]]\)], "Input"], Cell[BoxData[ \(TJIS[d_, 0, \ {{\[Beta]_, 0}, {\[Alpha]_, M_}, {\[Gamma]_, 0}}] := TJIS[d, 0, {{\[Alpha], M}, {\[Beta], 0}, {\[Gamma], 0}}]\)], "Input"], Cell[BoxData[ \(TJIS[d_, 0, \ {{\[Beta]_, 0}, {\[Gamma]_, 0}, {\[Alpha]_, M_}}] := TJIS[d, 0, {{\[Alpha], M}, {\[Beta], 0}, {\[Gamma], 0}}]\)], "Input"], Cell[BoxData[ \(TJIS[d_, 0, \ {{\[Alpha]_, M_}, {\[Beta]_, 0}, {\[Gamma]_, 0}}] := \n \(SMu\^2\/\((M\^2)\)\^\(\[Alpha] + \[Beta] + \[Gamma] - 4\)\) \(\((\(-1\))\)\^\(\[Alpha] + \[Beta] + \[Gamma] + 1\)\) \(Gamma[\[Alpha] + \[Beta] + \[Gamma] - d]\/\(Gamma[\[Alpha]] Gamma[\[Beta]] Gamma[\[Gamma]]\)\) \((Gamma[\[Beta] + \[Gamma] - d/2] Gamma[d/2 - \[Beta]] Gamma[d/2 - \[Gamma]])\)/Gamma[d/2]\)], "Input"], Cell[BoxData[ \(TJIS[d_, 0, \ {{\[Beta]_, M_}, {\[Alpha]_, 0}, {\[Gamma]_, M_}}] := TJIS[d, 0, {{\[Alpha], 0}, {\[Beta], M}, {\[Gamma], M}}]\)], "Input"], Cell[BoxData[ \(TJIS[d_, 0, \ {{\[Beta]_, M_}, {\[Gamma]_, M_}, {\[Alpha]_, 0}}] := TJIS[d, 0, {{\[Alpha], 0}, {\[Beta], M}, {\[Gamma], M}}]\)], "Input"], Cell[BoxData[ \(TJIS[d_, 0, \ {{\[Alpha]_, 0}, {\[Beta]_, M_}, {\[Gamma]_, M_}}] := \n \(SMu\^2\/\((M\^2)\)\^\(\[Alpha] + \[Beta] + \[Gamma] - 4\)\) \(\((\(-1\))\)\^\(\[Alpha] + \[Beta] + \[Gamma] + 1\)\) \(Gamma[\[Alpha] + \[Beta] + \[Gamma] - d]\/\(Gamma[\[Beta]] Gamma[\[Gamma]]\)\) \(Gamma[d\/2 - \[Alpha]]\/Gamma[d\/2]\) \(Gamma[\[Alpha] + \[Gamma] - d\/2] Gamma[\[Alpha] + \[Beta] - d\/2]\)\/Gamma[ 2 \[Alpha] + \[Beta] + \[Gamma] - d]\)], "Input"], Cell[BoxData[ \(TJIS[d_, 0, {{\[Alpha]_, 0}, {\[Beta]_, M_}, {\[Gamma]_, M_}}] := \((SMu\^2\ \((\(-1\))\)\^\(\[Alpha] + \[Beta] + \[Gamma] + 1\)\ Gamma[\[Alpha] + \[Beta] + \[Gamma] - d]\ Gamma[d\/2 - \[Alpha]]\ \((Gamma[\[Alpha] + \[Gamma] - d\/2]\ Gamma[\[Alpha] + \[Beta] - d\/2])\))\)/ \((\((M\^2)\)\^\(\[Alpha] + \[Beta] + \[Gamma] - 4\)\ \((Gamma[\[Beta]]\ Gamma[\[Gamma]])\)\ Gamma[d\/2]\ Gamma[2\ \[Alpha] + \[Beta] + \[Gamma] - d])\)\)], "Input"], Cell["(2.65)", "Text"], Cell[BoxData[ \(TAIS[d_, 0, {{1, M_}}] := \ \(-I\)\ \ M\^2\ \ SMu\ Gamma[\((4 - d)\)/2 - 1]\)], "Input"], Cell[BoxData[ \(\(TBIS[d_, 0, {{\[Alpha]_, 0}, {\[Beta]_, 0}}] := 0; \)\)], "Input"], Cell[BoxData[ \(\(TBIS[d_, Power[M_, \ 2], {{\[Alpha]_, 0}, {\[Beta]_, 0}}] := I\ SMu\ *\(( \(\((\(-1\))\)\^\(\[Alpha] + \[Beta]\)\/\((\(-\ M\^2\)) \)\^\(\[Alpha] + \[Beta] - 2\)\) Exp[\(-I\)\ Pi\ \((d - 4)\)/2]\ \(Gamma[\[Alpha] + \[Beta] - d/2]\/\(Gamma[\[Alpha]] Gamma[\[Beta]]\)\) \(Gamma[d/2 - \[Alpha]] Gamma[d/2 - \[Beta]]\)\/Gamma[ d - \[Alpha] - \[Beta]])\)\n\)\)], "Input"], Cell[BoxData[ \(TJIS[d_Symbol, M_\^2, {{1, M_}, {1, M_}, {1, M_}}] := M\^2\ SMu\^2\ \((\(-\(6\/\((\(-4\) + d)\)\^2\)\) + 17\/\(2\ \((\(-4\) + d)\)\) + 1\/8\ \((\(-59\) - 2\ \[Pi]\^2)\) + \((\(-4\) + d)\)\^3\ TJI111e + \(1\/1920\) \((\((\(-4\) + d)\)\^2\ \((16755 - 4750\ \[Pi]\^2 - 14\ \[Pi]\^4 + 3840\ \[Pi]\^2\ Log[2] - 12080\ Zeta[3])\))\) + 1\/96\ \((\(-4\) + d)\)\ \((195 + 98\ \[Pi]\^2 - 48\ Zeta[3])\)) \)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["TComment", "Subsection", CellTags->"T1.7.3.1"], Cell[BoxData[ \(\($CommentNotebook = True; \)\)], "Input"], Cell[BoxData[ \(TComment[s_String, b_] := If[If[\(\[InvisibleSpace]\(! \((ValueQ[$TarcerRecursed])\)\)\), $TarcerRecursed = {}]; \(\[InvisibleSpace]\(! \((MemberQ[$TarcerRecursed, {s, b}])\)\)\), AppendTo[$TarcerRecursed, {s, b}]; If[$Notebooks && $CommentNotebook === True, If[$commentnb === False, $commentnb = True; $cnb = NotebookCreate[ StyleDefinitions \[Rule] "\", Magnification \[Rule] 1.5]; SetOptions[$cnb, WindowMargins \[Rule] {{0, Automatic}, {Automatic, 0}}]; SetOptions[$cnb, WindowSize \[Rule] {333, 222}]; NotebookWrite[$cnb, Cell[BoxData[ ToBoxes[b /. TFIC \[Rule] TFI, TraditionalForm]], "\", CellDingbat \[Rule] s<>"\< \>"]], NotebookWrite[$cnb, Cell[BoxData[ ToBoxes[b /. TFIC \[Rule] TFI, TraditionalForm]], "\", CellDingbat \[Rule] s<>"\< \>"]]], Print[s, b /. {TFIC \[RuleDelayed] TFI, TVIC \[RuleDelayed] TVI, TJIC \[RuleDelayed] TJI, TBIC \[RuleDelayed] TBI, TAIC \[RuleDelayed] TAI}]]] /; $Comment === True\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["TarcerRecurse", "Subsection", CellTags->"T1.7.4.1"], Cell[BoxData[ \(\(FEPrint[a__String] := Print[a]\ /; \ $Notebooks === False; \)\)], "Input"], Cell[BoxData[ \(\(FEPrint[a__String] := If[Head[$cnb] === NotebookObject, \n\t\t NotebookWrite[$cnb, Cell[StringJoin@@{a}, "\"]]; \n\t SelectionMove[$cnb, After, Cell]] /; $Notebooks === True; \)\)], "Input"], Cell[BoxData[ RowBox[{ RowBox[{\(TarcerRecurse[z_]\), ":=", RowBox[{ StyleBox["Block", FontSize->16, FontWeight->"Bold", FontColor->RGBColor[1, 0.2, 0.2]], "[", RowBox[{ \({basisdone, fertig, dummm1, dummm2, getvars, te, fac, facfun, nexp, oldexpr, rec, sti, tl, tcheck, tvars, $cc = 0, $cv}\), ",", RowBox[{ \($commentnb = False\), ";", \(\((DownValues[facfun])\) =. \), ";", \(facfun[y_] := \(facfun[y] = If[FreeQ[y, Gamma], Factor[y], Factor[y] /. Plus \[RuleDelayed] \((Collect[\(+##1\), Gamma[__], Factor] /. Gamma \[RuleDelayed] \((Gamma[Factor[#1]]&)\)&) \)]\)\), ";", \(fac = \(( \((If[#1 > 1001, FEPrint[ "\"<> If[ValueQ[$cv], ToString[$cc], "\<\>"]<> If[ValueQ[$cv], "\< (\>"<>ToString[$cv]<>"\<)\>", "\<\>"]<> "\< factored, \>", ToString[#1]]]; #2)\)&)\)[ LeafCount[#1], \($cc++\); facfun[#1]]&\), ";", \(If[\(\[InvisibleSpace]\(! \((ValueQ[$TarcerRecursed])\)\)\), $TarcerRecursed = {}]\), ";", \($TarcerRecursed = {}\), ";", RowBox[{"If", "[", "\[InvisibleSpace]", RowBox[{ \(! \((MemberQ[$ContextPath, "\"])\)\), ",", \(t0 = z\), ",", RowBox[{"t0", "=", RowBox[{ \(HighEnergyPhysics`FeynCalc`ToTFi`ToTFi[z]\), "/.", RowBox[{"{", RowBox[{ RowBox[{ "HighEnergyPhysics`FeynCalc`TFi`TFi", "\[RuleDelayed]", StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]]}], ",", \(HighEnergyPhysics`FeynCalc`ToTFi`ToTFi \[RuleDelayed] Identity\)}], "}"}]}]}]}], "]"}], ";", RowBox[{"t0", "=", RowBox[{"Collect", "[", RowBox[{\(TFIRecurse[t0]\), ",", RowBox[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], "[", "__", "]"}], ",", "Factor"}], "]"}]}], ";", RowBox[{"getvars", "=", RowBox[{ RowBox[{"Select", "[", RowBox[{\(Variables[#1]\), ",", RowBox[{ RowBox[{"MatchQ", "[", RowBox[{"#1", ",", RowBox[{ RowBox[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], "[", "__", "]"}], "|", RowBox[{ StyleBox["TVI", FontColor->RGBColor[0.2, 0.4, 0.8]], "[", "__", "]"}], "|", \(TJI[__]\), "|", \(TBI[__]\), "|", \(TAI[__]\)}]}], "]"}], "&"}]}], "]"}], "&"}]}], ";", \(rec[expr_, {ti_, tr_}] := \((sti = ToString[ti]; tcheck = \(\[InvisibleSpace]\(! \((FreeQ[expr, ti])\)\)\); oldexpr =. ; nexp = expr; While[tcheck === True && oldexpr =!= nexp, oldexpr = nexp; If[$Comment, \((If[#1 === 1, FEPrint[sti<>"\< level, there is 1 \>"<>sti], FEPrint[sti<>"\< level, there are \>", ToString[#1], "\< \>"<>sti<>"\<'s \>"]]&)\)[ Count[nexp, ti[__], \(-1\)]]]; nexp = \(nexp /. ti \[Rule] tr\) /. tr \[Rule] ti; tvars = getvars[nexp]; $cc = 0; $cv = Length[tvars]; nexp = Collect[nexp, tvars, fac]; tcheck = \(\[InvisibleSpace]\(! \((FreeQ[nexp, ti])\)\)\); ]; nexp)\)\), ";", \(basisdone = 0\), ";", RowBox[{"tl", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ StyleBox["TFI", FontColor->RGBColor[1, 0.6, 0]], ",", StyleBox["TFR", FontColor->RGBColor[0, 0.6, 0]]}], "}"}], ",", RowBox[{"{", RowBox[{ StyleBox["TVI", FontColor->RGBColor[0.2, 0.4, 0.8]], ",", StyleBox["TVR", FontColor->RGBColor[0.2, 0.8, 1]]}], "}"}], ",", \({TJI, TJR}\), ",", \({TBI, TBR}\), ",", \({TAI, TAR}\)}], "}"}]}], ";", \(Do[\((DownValues[facfun])\) =. ; facfun[y_] := \(facfun[y] = If[FreeQ[y, Gamma], Factor[y], Factor[y] /. Plus \[RuleDelayed] \((Collect[\(+##1\), Gamma[__], Factor] /. Gamma \[RuleDelayed] \((Gamma[Factor[#1]]&)\)&)\)]\); t0 = rec[t0, tl\[LeftDoubleBracket]i\[RightDoubleBracket]]; If[Head[t0] === Plus, fertig = Select[t0, \(\[InvisibleSpace]\(! \((FreeQ[#1, tl\[LeftDoubleBracket]i, 1\[RightDoubleBracket]]) \)\)\)]; basisdone = basisdone + fertig; t0 = t0 - fertig], {i, Length[tl]}]\), ";", \(t0 = t0 + basisdone\), ";", \(If[Head[t0] === Plus, $cv =. ; t0 = Select[t0, FreeQ[#1, TAI]&] + Collect[ Select[t0, \(\[InvisibleSpace]\(! \((FreeQ[#1, TAI])\)\)\)&], { TAI[__], TAI[a1__]\ TAI[a2__], TAI[__], TBI[__]}, fac]]\), ";", \(If[$Comment, FEPrint["\", ToString[Length[t0 + dummm1 + dummm2] - 2], "\< terms\>"]] \), ";", \(If[$Notebooks, SetSelectedNotebook[EvaluationNotebook[]]]\), ";", "t0"}]}], "]"}]}], ";"}]], "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["TarcerExpand", "Section", CellDingbat->"\[FilledSmallCircle]", CellTags->"T1.8.1"], Cell[BoxData[ \(\(Options[TarcerExpand] = {\n\t\tTarcerReduce :> $BasisIntegrals, \n\t TarcerRecurse -> False, Zeta -> True}; \)\)], "Input"], Cell[BoxData[ \(\(TarcerExpand[expr_, d_Symbol -> fe_ /; Length[Variables[fe]] === 1, ru___Rule] := TarcerExpand[expr, d\ -> fe, 0, ru]; \)\)], "Input"], Cell[BoxData[ \(TarcerExpand[expr_, d_Symbol \[Rule] fe_ /; Length[Variables[fe]] === 1, order_Integer?NonNegative, opts___Rule] := Block[{}, Catch[e = First[Variables[fe]]; {ints, recurse, zeta2replace} = {TarcerReduce, TarcerRecurse, Zeta} /. Flatten[{opts, Options[TarcerExpand]}]; If[zeta2replace =!= True && MemberQ[$ContextPath, "\"], z2rule = {}, z2rule = \[Pi]\^2 \[RuleDelayed] 6\ ToExpression[ "\"]]; ints = Flatten[ints]; If[recurse =!= True, ta0 = expr, ta0 = TarcerRecurse[expr]]; t1 = \(ta0 /. ints\) /. PreFactor[any_] \[RuleDelayed] PreFactor[any /. d -> dummyd]; \n \n\t\t\tvars = Select[Variables[t1], Length[#1] > 0&]; If[\(\[InvisibleSpace]\(! \((FreeQ[vars, TFI | TVI | TJI | TKI | TBI | TAI])\)\)\), Print["\"]; Throw[Select[vars, \(\[InvisibleSpace]\(! \((FreeQ[#1, TFI | TVI | TJI | TKI | TBI | TAI]) \)\)\)&]]]; \n\t\t\tt1 = t1 /. d \[Rule] fe; \n\t\t\t polygafu[2, 1] = \(-2\)\ Zeta[3]; polygafu[2, 2] = 2 - 2\ Zeta[3]; polygafu[x_, y_] := \(polygafu[x, y] = FunctionExpand[PolyGamma[x, y]]\); t2 = Normal[t1 + O[e]\^\(order + 1\)] /. PolyGamma \[Rule] polygafu; t3 = \(Collect[t2, e, Expand[#1] /. z2rule&] //. { PreFactor[a_]\ PreFactor[b_] \[RuleDelayed] PreFactor[a\ b]} \) /. PreFactor[c_] \[RuleDelayed] PreFactor[c /. dummyd -> fe]; prec = Union[Cases[t3, PreFactor[_], \(-1\)]]; \n\n\t\t\t\n\t\t\t If[Length[prec] === 1, If[Head[t3] === Plus, mass = Select[ Variables[ prec\[LeftDoubleBracket]1, 1\[RightDoubleBracket]], FreeQ[#1, SEpsilon]&]; \n\n\t\t\t\t\t\n\t\t\t\t\t If[Length[mass] === 1, If[FreeQ[First[t3], First[mass]], massfactor = 1, massfactor = First[mass]\^Exponent[First[t3], First[mass]]], massfactor = 1]; \n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t delpfactor = 1; delp = Variables[ First[t3]\/massfactor /. {PreFactor[__] \[RuleDelayed] 1, ToExpression[ "\"] \[Rule] Zeta[2]}]; \n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t If[Length[delp] === 1, delp = First[delp]; If[Length[t3] === Length[Select[t3, \[InvisibleSpace]\(! \((FreeQ[#1, delp])\)\)&]], delpfactor = delp\^Exponent[First[t3], delp]]]; t3 = \((\(massfactor\ delpfactor\ First[prec] /. PreFactor \[Rule] Identity\) /. { \((m_\^2)\)\^n_\ m_\^j_?EvenQ \[RuleDelayed] \((m\^2)\)\^\(n + j\/2\)})\)\ Collect[ \((#1/\((\((First[prec]\ massfactor)\)\ delpfactor)\)&) \)/@t3, e, Expand]]]; t3 /. PreFactor \[Rule] Identity]]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Construct T's", "Section", CellDingbat->"\[FilledSmallCircle]", CellTags->"T1.9.1"], Cell[CellGroupData[{ Cell["remember", "Subsection", CellTags->"T1.9.1.1"], Cell["The function remember is not used by default.", "Text"], Cell[BoxData[ \(\(tfch = {TFR :> Hold[TFR], TVR :> Hold[TVR], TJR :> Hold[TJR], TBR :> Hold[TBR], TAR :> Hold[TAR], TComment :> Hold[TComment]}; \)\)], "Input"], Cell[BoxData[ \(\(rtfch = Map[Reverse, tfch]; \)\)], "Input"], Cell[BoxData[{ \(\(SetAttributes[condrest, HoldRest]; \)\), \(\(Clear[remember]; \)\), \(\(remember[zi_HoldForm] := Block[{z = zi /. tfch}, If[\(\[InvisibleSpace]\(! \((FreeQ[z, Condition])\)\)\), \(\(\(\(Hold[HoldForm]\)[ \(Hold[SetDelayed]\)[ z\[LeftDoubleBracket]1, 1\[RightDoubleBracket], ReplacePart[ z\[LeftDoubleBracket]1, 2\[RightDoubleBracket], Prepend[Extract[z, {1, 2, 1}, Hold], \(\(\(z\[LeftDoubleBracket]1, 1 \[RightDoubleBracket] /. PatternTest \[Rule] pt\) /. pt[a_, b_] \[RuleDelayed] a\) /. Pattern \[Rule] pat\) /. pat[a_, b_] \[RuleDelayed] a], 1]]] /. Hold[HoldForm] \[Rule] HoldForm\) /. rtfch\) /. Hold[SetDelayed] \[Rule] SetDelayed\) /. Hold \[Rule] Set, \(\(\(\(Hold[HoldForm]\)[ \(Hold[SetDelayed]\)[ z\[LeftDoubleBracket]1, 1\[RightDoubleBracket], Prepend[Extract[z, {1, 2}, Hold], \(\(\(z\[LeftDoubleBracket]1, 1 \[RightDoubleBracket] /. PatternTest \[Rule] pt\) /. pt[a_, b_] \[RuleDelayed] a\) /. Pattern \[Rule] pat\) /. pat[a_, b_] \[RuleDelayed] a]]] /. Hold[HoldForm] \[Rule] HoldForm\) /. rtfch\) /. Hold[SetDelayed] \[Rule] SetDelayed\) /. Hold \[Rule] Set]]; \)\)}], "Input"], Cell[BoxData[ \($TarasovTdeltaplimit\)], "Input"], Cell[BoxData[ \(\(aa2\ = \ Array[f\_#&, \ 10000 + \(($TarasovTdeltaplimit + 1)\)\ 1000]; \)\)], "Input"], Cell[BoxData[ \(\(bb12 = Select[aa2, Head[#] =!= Subscript&]; \)\)], "Input"], Cell[BoxData[ \(Print["\", Length[bb12], "\< recursion equations for $RankLimit = \>", $RankLimit]\)], "Input"], Cell["\<\ Change DONTremember to remember in order to use the remember function.\ \>", "Text"], Cell[BoxData[ \(\(nb\ = Map[DONTremember, bb12]; \)\)], "Input"], Cell[BoxData[ \(\(ReleaseHold[nb]; \)\)], "Input"], Cell[BoxData[ \(Unset[$Post]\)], "Input"], Cell[BoxData[ \(\($Comment = True; \)\)], "Input"], Cell[BoxData[ \(\(End[]; \)\)], "Input"], Cell[BoxData[ \(\(EndPackage[]; \)\)], "Input"], Cell[BoxData[ \(\(BeginPackage["\"]; \)\)], "Input"], Cell[BoxData[ \(\(Zeta2::usage = \n"\"; \)\)], "Input"], Cell[BoxData[ \(Begin["\<`Private`\>"]; \n\ \ \ SetAttributes[Zeta2, \ ReadProtected]; \)], "Input"], Cell[BoxData[ \(\(Zeta2\ /: \ N[Zeta2]\ = \ N[Zeta[2]]; \)\)], "Input"], Cell[BoxData[ \(Zeta2 /: MakeBoxes[Zeta2, fmt_] := InterpretationBox@@{\ \ RowBox[{"\<\[Zeta]\>", "\<(\>", 2, "\<)\>"}], Zeta2, Editable -> False}\)], "Input"], Cell[BoxData[ \(\(End[]; \)\)], "Input"], Cell[BoxData[ \(\(\ \(EndPackage[]; \)\)\)], "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["$BasisIntegrals", "Section", CellDingbat->"\[EmptySmallCircle]", CellTags->"T1.10.1"], Cell["\<\ This a (incomplete) set of basis integrals. You can add your favorite \ integrals here.\ \>", "Text"], Cell["\<\ $BasisIntegrals = {TAI[d_, 0, {{1, M_}}] :> -I*E^(1/2*(4 - d)*EulerGamma)*M^2* Gamma[-1 + (4 - d)/2]* PreFactor[(M^2)^(1/2*(-4 + d))* SEpsilon[d]], TBI[d_, pp_, {{1, 0},{1, 0}}] :> (I*E^(((4 - d)*EulerGamma)/2 - I/2*(-4 + d)*Pi)*Gamma[2 - d/2]* Gamma[-1 + d/2]^2* PreFactor[(pp)^((-4 + d)/2)* SEpsilon[d]])/Gamma[-2 + d], TJI[d_, pp_, {{1,0},{1,0},{1,0}}] :>-((pp*Gamma[3 - d]*Gamma[-1 + \ d/2]^3* E^((4 - d)*EulerGamma)* PreFactor[ (pp)^(-4 + d)*SEpsilon[d]^2])/ (E^(I*(-4 + d)*Pi)*Gamma[-3 + (3*d)/2]) ), TJI[d_, M_^2, {{1,M_},{1,0},{1,0}}] :>(M^2*Gamma[3 - d]*Gamma[2 - \ d/2]* Gamma[-1 + d/2]^2*Gamma[-5 + 2*d]*E^((4 - d)*EulerGamma)* PreFactor[ (M^2)^(-4 + d)*SEpsilon[d]^2])/ (Gamma[-2 + d]*Gamma[-3 + (3*d)/2]), TJI[d_Symbol, (M_)^2, {{1, M_}, {1, M_}, {1, M_}}]:>M^2*PreFactor[ (M^2)^(-4 + d)*SEpsilon[d]^2]* (-6/(-4 + d)^2 + 17/(2*(-4 + d)) + (-59 - 2*Pi^2)/8 + (-4 + d)^3*TJI111e + ((-4 + d)^2*(16755 - 4750*Pi^2 - 14*Pi^4 + 3840*Pi^2*Log[2] - 12080*Zeta[3]))/1920 + ((-4 + d)*(195 + 98*Pi^2 - 48*Zeta[3]))/96), TJI[d_, 0, {{1, M_}, {1, M_}, {1, 0}}]:>(M^2*Gamma[3 - d]*Gamma[2 - \ d/2]^2* Gamma[-1 + d/2]*E^((4 - d)*EulerGamma)* PreFactor[ (M^2)^(-4 + d)*SEpsilon[d]^2])/ (Gamma[4 - d]*Gamma[d/2]), TJI[d_, 0, {{1,M_},{1,0},{1,0}}] :>(M^2*Gamma[3 - d]*Gamma[2 - d/2]* Gamma[-1 + d/2]^2*E^((4 - d)*EulerGamma)* PreFactor[ (M^2)^(-4 + d)*SEpsilon[d]^2])/ Gamma[d/2] }\ \>", "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Save tarcer*.mx file", "Section", CellDingbat->"\[FilledSmallCircle]", CellTags->"T1.11.1"], Cell[BoxData[ \(\(Share[]; \)\)], "Input"], Cell[BoxData[ \(\(DumpSave[ "\"<>\((Apply[StringJoin, ToString/@$RankLimit])\)<> "\<.mx\>", {$ContextPath, HighEnergyPhysics`Tarcer`Cayley, \ HighEnergyPhysics`Tarcer`CayleyD, \ HighEnergyPhysics`Tarcer`Cayleyu, \ \n\t\t\ HighEnergyPhysics`Tarcer`PreFactor, \n\ \ HighEnergyPhysics`Tarcer`TarcerRecurse, \n\t\t HighEnergyPhysics`Tarcer`TFIRecurse, \ HighEnergyPhysics`Tarcer`SEpsilon, \ \ HighEnergyPhysics`Tarcer`TarcerExpand, HighEnergyPhysics`Tarcer`TarcerReduce, \ HighEnergyPhysics`Tarcer`TAI, \ HighEnergyPhysics`Tarcer`TAR, \ HighEnergyPhysics`Tarcer`TBI, \ \n\ \ HighEnergyPhysics`Tarcer`TBR, \ HighEnergyPhysics`Tarcer`TFI, \ HighEnergyPhysics`Tarcer`TFR, \ HighEnergyPhysics`Tarcer`TJI, \ \n\ \ HighEnergyPhysics`Tarcer`TJR, \ HighEnergyPhysics`Tarcer`TKI, \ HighEnergyPhysics`Tarcer`TVI, \ HighEnergyPhysics`Tarcer`TVR, \ \n\t\t\ \ HighEnergyPhysics`Tarcer`$BasisIntegrals, \ \n\ \ HighEnergyPhysics`Tarcer`$Comment, \n\t\t\ \ HighEnergyPhysics`Tarcer`$CommentNotebook, \ \ HighEnergyPhysics`Tarcer`$RankLimit, \n\t\t\n\t HighEnergyPhysics`Tarcer`Private`ExpandMaybe, \ HighEnergyPhysics`Tarcer`Private`FactorC, \ \n\t\t HighEnergyPhysics`Tarcer`Private`FEPrint, \ \n\ \ HighEnergyPhysics`Tarcer`Private`fN, \ \n\t\ \ HighEnergyPhysics`Tarcer`Private`mbt, \t\n\t\t HighEnergyPhysics`Tarcer`Private`PNQ, \ \n\ \ HighEnergyPhysics`Tarcer`Private`PQ, \ HighEnergyPhysics`Tarcer`Private`ta, \ HighEnergyPhysics`Tarcer`Private`TA, \ \n\ \ HighEnergyPhysics`Tarcer`Private`TAIC, \ HighEnergyPhysics`Tarcer`Private`TBIC, \ \n\t\t HighEnergyPhysics`Tarcer`Private`TComment, \ \n\t\t\n\t\t HighEnergyPhysics`Tarcer`Private`TLRComment, \ \n\ \ HighEnergyPhysics`Tarcer`Private`TFIC, \ \n\ \ HighEnergyPhysics`Tarcer`Private`TJIC, \ HighEnergyPhysics`Tarcer`Private`TLR, \ \n\ \ HighEnergyPhysics`Tarcer`Private`tlrule, \ \n\t\t\ \ HighEnergyPhysics`Tarcer`Private`redblue, \n\t\t HighEnergyPhysics`Tarcer`Private`TLRules, \ \n\ \ HighEnergyPhysics`Tarcer`Private`TVIC, \ HighEnergyPhysics`Tarcer`Private`$TLRComment, \n\t\t\n\t\t HighEnergyPhysics`FeynCalc`Zeta2`Zeta2\n\t\t\n\t}]; \)\)], "Input", Editable->False], Cell["\<\ This gives the absolute time (in minutes) to run this notebook.\ \>", "Text"], Cell[BoxData[ \(Round[AbsoluteTime[] - HighEnergyPhysics`Tarcer`Private`atime]/60. \ min \)], "Input"], Cell["Display the size of the generated file:", "Text"], Cell[BoxData[ \(filename\ = \ "\"<>\((Apply[StringJoin, ToString/@$RankLimit])\)<> "\<.mx\>"\)], "Input"], Cell[BoxData[ \(FileByteCount[filename]\ Byte\)], "Input"], Cell[BoxData[ \(Directory[]\)], "Input"], Cell[BoxData[ \(MaxMemoryUsed[]\)], "Input"], Cell[BoxData[ \(MemoryInUse[]\)], "Input"] }, Closed]] }, Open ]] }, FrontEndVersion->"X 3.0", ScreenRectangle->{{0, 1504}, {0, 1128}}, AutoGeneratedPackage->None, ScreenStyleEnvironment->"AllBrackets", WindowToolbars->"EditBar", WindowSize->{552, 400}, WindowMargins->{{223, Automatic}, {Automatic, 222}}, PrintingPageRange->{Automatic, Automatic}, PrintingOptions->{"PaperSize"->{597.562, 842.375}, "PaperOrientation"->"Portrait", "Magnification"->1}, TaggingRules:>{"Version1.0(Jan 22 1998) R. Mertig and R. Scharf"}, Magnification->1, StyleDefinitions -> "Default.nb" ] (*********************************************************************** Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. ***********************************************************************) (*CellTagsOutline CellTagsIndex->{ "T1.1"->{ Cell[1731, 51, 72, 2, 107, "Title", CellTags->"T1.1"]}, "T1.2"->{ Cell[1986, 63, 434, 14, 104, "Text", CellTags->"T1.2"]}, "T1.1.1"->{ Cell[40466, 1268, 93, 2, 34, "Section", CellTags->"T1.1.1"]}, "T1.2.1.1"->{ Cell[43780, 1373, 78, 1, 40, "Subsubsection", CellTags->"T1.2.1.1"]}, "T1.2.1"->{ Cell[44422, 1393, 86, 2, 34, "Section", CellTags->"T1.2.1"]}, "T1.3.1"->{ Cell[50074, 1550, 112, 2, 34, "Section", CellTags->"T1.3.1"]}, "T1.3.1.1"->{ Cell[52128, 1623, 63, 1, 45, "Subsection", CellTags->"T1.3.1.1"]}, "T1.3.2.1"->{ Cell[74599, 2118, 58, 1, 46, "Subsection", CellTags->"T1.3.2.1"]}, "T1.3.3.1"->{ Cell[79012, 2198, 59, 1, 46, "Subsection", CellTags->"T1.3.3.1"]}, "T1.3.4.1"->{ Cell[82587, 2281, 60, 1, 46, "Subsection", CellTags->"T1.3.4.1"]}, "T1.3.5.1"->{ Cell[83442, 2307, 54, 1, 46, "Subsection", CellTags->"T1.3.5.1"]}, "T1.3.6.1"->{ Cell[88034, 2405, 59, 1, 46, "Subsection", CellTags->"T1.3.6.1"]}, "T1.3.7.1"->{ Cell[88593, 2421, 50, 1, 46, "Subsection", CellTags->"T1.3.7.1"]}, "T1.3.7.1.1"->{ Cell[88755, 2429, 57, 1, 40, "Subsubsection", CellTags->"T1.3.7.1.1"]}, "T1.3.7.2.1"->{ Cell[91453, 2499, 53, 1, 40, "Subsubsection", CellTags->"T1.3.7.2.1"]}, "T1.3.7.3.1"->{ Cell[91618, 2508, 54, 1, 40, "Subsubsection", CellTags->"T1.3.7.3.1"]}, "T1.3.7.4.1"->{ Cell[91840, 2520, 58, 1, 40, "Subsubsection", CellTags->"T1.3.7.4.1"]}, "T1.3.7.5.1"->{ Cell[92016, 2529, 54, 1, 40, "Subsubsection", CellTags->"T1.3.7.5.1"]}, "T1.3.7.6.1"->{ Cell[94283, 2571, 54, 1, 40, "Subsubsection", CellTags->"T1.3.7.6.1"]}, "T1.3.7.7.1"->{ Cell[94800, 2595, 54, 1, 40, "Subsubsection", CellTags->"T1.3.7.7.1"]}, "T1.3.7.8.1"->{ Cell[95537, 2620, 54, 1, 40, "Subsubsection", CellTags->"T1.3.7.8.1"]}, "T1.4.1"->{ Cell[95870, 2636, 104, 2, 34, "Section", CellTags->"T1.4.1"]}, "T1.4.1.1"->{ Cell[97903, 2688, 116, 3, 46, "Subsection", CellTags->"T1.4.1.1"]}, "T1.4.2.1"->{ Cell[98347, 2707, 114, 3, 46, "Subsection", CellTags->"T1.4.2.1"]}, "T1.4.3.1"->{ Cell[100569, 2776, 205, 6, 46, "Subsection", CellTags->"T1.4.3.1"]}, "T1.4.4.1"->{ Cell[105308, 2900, 223, 6, 56, "Subsection", CellTags->"T1.4.4.1"]}, "T1.5.1"->{ Cell[117690, 3221, 97, 2, 34, "Section", CellTags->"T1.5.1"]}, "T1.5.1.1"->{ Cell[117812, 3227, 65, 1, 46, "Subsection", CellTags->"T1.5.1.1"]}, "T1.5.1.1.1"->{ Cell[181979, 4483, 62, 1, 40, "Subsubsection", CellTags->"T1.5.1.1.1"]}, "T1.5.2.1"->{ Cell[185363, 4568, 69, 1, 46, "Subsection", CellTags->"T1.5.2.1"]}, "T1.5.2.1.1"->{ Cell[186757, 4599, 53, 1, 40, "Subsubsection", CellTags->"T1.5.2.1.1"]}, "T1.5.3.1"->{ Cell[192456, 4743, 60, 1, 46, "Subsection", CellTags->"T1.5.3.1"]}, "T1.5.3.1.1"->{ Cell[192860, 4758, 68, 1, 40, "Subsubsection", CellTags->"T1.5.3.1.1"]}, "T1.5.3.2.1"->{ Cell[195819, 4821, 68, 1, 40, "Subsubsection", CellTags->"T1.5.3.2.1"]}, "T1.6.1"->{ Cell[198221, 4878, 140, 2, 56, "Section", CellTags->"T1.6.1"]}, "T1.6.1.1"->{ Cell[198655, 4893, 56, 1, 46, "Subsection", CellTags->"T1.6.1.1"]}, "T1.6.2.1"->{ Cell[206258, 5080, 58, 1, 46, "Subsection", CellTags->"T1.6.2.1"]}, "T1.6.2.1.1"->{ Cell[206425, 5088, 131, 5, 40, "Subsubsection", CellTags->"T1.6.2.1.1"]}, "T1.6.2.2.1"->{ Cell[207678, 5128, 131, 5, 40, "Subsubsection", CellTags->"T1.6.2.2.1"]}, "T1.6.2.3.1"->{ Cell[209012, 5170, 131, 5, 40, "Subsubsection", CellTags->"T1.6.2.3.1"]}, "T1.6.2.4.1"->{ Cell[210346, 5212, 131, 5, 40, "Subsubsection", CellTags->"T1.6.2.4.1"]}, "T1.6.3.1"->{ Cell[211692, 5255, 58, 1, 46, "Subsection", CellTags->"T1.6.3.1"]}, "T1.6.4.1"->{ Cell[215485, 5362, 159, 5, 46, "Subsection", CellTags->"T1.6.4.1"]}, "T1.6.5.1"->{ Cell[216130, 5386, 58, 1, 46, "Subsection", CellTags->"T1.6.5.1"]}, "T1.6.6.1"->{ Cell[219923, 5493, 159, 5, 46, "Subsection", CellTags->"T1.6.6.1"]}, "T1.6.7.1"->{ Cell[220568, 5517, 159, 5, 46, "Subsection", CellTags->"T1.6.7.1"]}, "T1.6.8.1"->{ Cell[221355, 5546, 159, 5, 46, "Subsection", CellTags->"T1.6.8.1"]}, "T1.6.9.1"->{ Cell[222142, 5575, 56, 1, 46, "Subsection", CellTags->"T1.6.9.1"]}, "T1.6.10.1"->{ Cell[228991, 5744, 59, 1, 46, "Subsection", CellTags->"T1.6.10.1"]}, "T1.6.11.1"->{ Cell[230250, 5783, 57, 1, 46, "Subsection", CellTags->"T1.6.11.1"]}, "T1.6.12.1"->{ Cell[234553, 5911, 57, 1, 46, "Subsection", CellTags->"T1.6.12.1"]}, "T1.6.13.1"->{ Cell[238856, 6039, 57, 1, 46, "Subsection", CellTags->"T1.6.13.1"]}, "T1.6.14.1"->{ Cell[246331, 6220, 68, 1, 46, "Subsection", CellTags->"T1.6.14.1"]}, "T1.6.15.1"->{ Cell[246744, 6236, 59, 1, 46, "Subsection", CellTags->"T1.6.15.1"]}, "T1.6.16.1"->{ Cell[269498, 6780, 57, 1, 46, "Subsection", CellTags->"T1.6.16.1"]}, "T1.6.17.1"->{ Cell[273531, 6893, 59, 1, 46, "Subsection", CellTags->"T1.6.17.1"]}, "T1.6.18.1"->{ Cell[274210, 6920, 57, 1, 46, "Subsection", CellTags->"T1.6.18.1"]}, "T1.6.19.1"->{ Cell[279722, 7068, 59, 1, 46, "Subsection", CellTags->"T1.6.19.1"]}, "T1.6.20.1"->{ Cell[280378, 7093, 59, 1, 46, "Subsection", CellTags->"T1.6.20.1"]}, "T1.6.21.1"->{ Cell[281068, 7119, 57, 1, 46, "Subsection", CellTags->"T1.6.21.1"]}, "T1.6.22.1"->{ Cell[284489, 7219, 59, 1, 46, "Subsection", CellTags->"T1.6.22.1"]}, "T1.6.23.1"->{ Cell[285099, 7242, 57, 1, 46, "Subsection", CellTags->"T1.6.23.1"]}, "T1.6.24.1"->{ Cell[289233, 7359, 59, 1, 46, "Subsection", CellTags->"T1.6.24.1"]}, "T1.6.25.1"->{ Cell[289867, 7383, 57, 1, 46, "Subsection", CellTags->"T1.6.25.1"]}, "T1.6.26.1"->{ Cell[293554, 7489, 59, 1, 46, "Subsection", CellTags->"T1.6.26.1"]}, "T1.6.27.1"->{ Cell[294190, 7513, 57, 1, 46, "Subsection", CellTags->"T1.6.27.1"]}, "T1.6.28.1"->{ Cell[299511, 7657, 59, 1, 46, "Subsection", CellTags->"T1.6.28.1"]}, "T1.6.29.1"->{ Cell[300513, 7687, 58, 1, 46, "Subsection", CellTags->"T1.6.29.1"]}, "T1.6.30.1"->{ Cell[303935, 7787, 59, 1, 46, "Subsection", CellTags->"T1.6.30.1"]}, "T1.6.31.1"->{ Cell[304564, 7810, 58, 1, 46, "Subsection", CellTags->"T1.6.31.1"]}, "T1.6.32.1"->{ Cell[309787, 7973, 59, 1, 46, "Subsection", CellTags->"T1.6.32.1"]}, "T1.6.33.1"->{ Cell[310935, 8020, 61, 1, 46, "Subsection", CellTags->"T1.6.33.1"]}, "T1.6.34.1"->{ Cell[312129, 8067, 58, 1, 46, "Subsection", CellTags->"T1.6.34.1"]}, "T1.6.35.1"->{ Cell[317744, 8224, 59, 1, 46, "Subsection", CellTags->"T1.6.35.1"]}, "T1.6.36.1"->{ Cell[318981, 8264, 58, 1, 46, "Subsection", CellTags->"T1.6.36.1"]}, "T1.6.37.1"->{ Cell[325698, 8431, 59, 1, 46, "Subsection", CellTags->"T1.6.37.1"]}, "T1.6.38.1"->{ Cell[327408, 8493, 61, 1, 46, "Subsection", CellTags->"T1.6.38.1"]}, "T1.6.39.1"->{ Cell[329229, 8552, 61, 1, 46, "Subsection", CellTags->"T1.6.39.1"]}, "T1.6.40.1"->{ Cell[330323, 8590, 61, 1, 46, "Subsection", CellTags->"T1.6.40.1"]}, "T1.6.41.1"->{ Cell[331179, 8620, 58, 1, 46, "Subsection", CellTags->"T1.6.41.1"]}, "T1.6.42.1"->{ Cell[336272, 8759, 59, 1, 46, "Subsection", CellTags->"T1.6.42.1"]}, "T1.6.43.1"->{ Cell[337046, 8786, 68, 1, 46, "Subsection", CellTags->"T1.6.43.1"]}, "T1.6.44.1"->{ Cell[342806, 8946, 57, 1, 46, "Subsection", CellTags->"T1.6.44.1"]}, "T1.6.45.1"->{ Cell[357469, 9356, 59, 1, 46, "Subsection", CellTags->"T1.6.45.1"]}, "T1.6.46.1"->{ Cell[358201, 9383, 61, 1, 46, "Subsection", CellTags->"T1.6.46.1"]}, "T1.6.47.1"->{ Cell[358981, 9410, 57, 1, 46, "Subsection", CellTags->"T1.6.47.1"]}, "T1.6.48.1"->{ Cell[365003, 9566, 59, 1, 46, "Subsection", CellTags->"T1.6.48.1"]}, "T1.6.49.1"->{ Cell[365747, 9593, 61, 1, 46, "Subsection", CellTags->"T1.6.49.1"]}, "T1.6.50.1"->{ Cell[366543, 9620, 57, 1, 46, "Subsection", CellTags->"T1.6.50.1"]}, "T1.6.51.1"->{ Cell[379090, 9929, 59, 1, 46, "Subsection", CellTags->"T1.6.51.1"]}, "T1.6.52.1"->{ Cell[379771, 9956, 57, 1, 46, "Subsection", CellTags->"T1.6.52.1"]}, "T1.6.53.1"->{ Cell[385171, 10103, 59, 1, 46, "Subsection", CellTags->"T1.6.53.1"]}, "T1.6.54.1"->{ Cell[385612, 10122, 61, 1, 46, "Subsection", CellTags->"T1.6.54.1"]}, "T1.6.55.1"->{ Cell[386088, 10141, 61, 1, 46, "Subsection", CellTags->"T1.6.55.1"]}, "T1.6.56.1"->{ Cell[386564, 10160, 57, 1, 46, "Subsection", CellTags->"T1.6.56.1"]}, "T1.6.57.1"->{ Cell[392439, 10321, 59, 1, 46, "Subsection", CellTags->"T1.6.57.1"]}, "T1.6.58.1"->{ Cell[392832, 10338, 57, 1, 46, "Subsection", CellTags->"T1.6.58.1"]}, "T1.6.59.1"->{ Cell[397467, 10464, 59, 1, 46, "Subsection", CellTags->"T1.6.59.1"]}, "T1.6.60.1"->{ Cell[397878, 10483, 57, 1, 46, "Subsection", CellTags->"T1.6.60.1"]}, "T1.6.61.1"->{ Cell[402993, 10622, 59, 1, 46, "Subsection", CellTags->"T1.6.61.1"]}, "T1.6.62.1"->{ Cell[403497, 10642, 61, 1, 46, "Subsection", CellTags->"T1.6.62.1"]}, "T1.6.63.1"->{ Cell[404045, 10663, 61, 1, 46, "Subsection", CellTags->"T1.6.63.1"]}, "T1.6.64.1"->{ Cell[404610, 10684, 57, 1, 46, "Subsection", CellTags->"T1.6.64.1"]}, "T1.6.65.1"->{ Cell[415136, 10946, 59, 1, 46, "Subsection", CellTags->"T1.6.65.1"]}, "T1.6.66.1"->{ Cell[415600, 10966, 61, 1, 46, "Subsection", CellTags->"T1.6.66.1"]}, "T1.6.67.1"->{ Cell[416105, 10986, 61, 1, 46, "Subsection", CellTags->"T1.6.67.1"]}, "T1.6.68.1"->{ Cell[416610, 11006, 57, 1, 46, "Subsection", CellTags->"T1.6.68.1"]}, "T1.6.69.1"->{ Cell[423512, 11181, 59, 1, 46, "Subsection", CellTags->"T1.6.69.1"]}, "T1.6.70.1"->{ Cell[423969, 11201, 57, 1, 46, "Subsection", CellTags->"T1.6.70.1"]}, "T1.6.70.1.1"->{ Cell[424051, 11206, 56, 1, 40, "Subsubsection", CellTags->"T1.6.70.1.1"]}, "T1.6.70.2.1"->{ Cell[425781, 11258, 56, 1, 40, "Subsubsection", CellTags->"T1.6.70.2.1"]}, "T1.6.71.1"->{ Cell[432197, 11436, 59, 1, 46, "Subsection", CellTags->"T1.6.71.1"]}, "T1.6.72.1"->{ Cell[432546, 11453, 57, 1, 46, "Subsection", CellTags->"T1.6.72.1"]}, "T1.6.73.1"->{ Cell[441844, 11677, 59, 1, 46, "Subsection", CellTags->"T1.6.73.1"]}, "T1.6.74.1"->{ Cell[442190, 11693, 57, 1, 46, "Subsection", CellTags->"T1.6.74.1"]}, "T1.6.75.1"->{ Cell[453670, 12015, 60, 1, 46, "Subsection", CellTags->"T1.6.75.1"]}, "T1.6.76.1"->{ Cell[454052, 12032, 60, 1, 46, "Subsection", CellTags->"T1.6.76.1"]}, "T1.6.77.1"->{ Cell[454502, 12051, 60, 1, 46, "Subsection", CellTags->"T1.6.77.1"]}, "T1.6.78.1"->{ Cell[454893, 12068, 60, 1, 46, "Subsection", CellTags->"T1.6.78.1"]}, "T1.6.79.1"->{ Cell[455315, 12085, 57, 1, 46, "Subsection", CellTags->"T1.6.79.1"]}, "T1.6.80.1"->{ Cell[460594, 12222, 57, 1, 46, "Subsection", CellTags->"T1.6.80.1"]}, "T1.6.81.1"->{ Cell[463087, 12298, 59, 1, 46, "Subsection", CellTags->"T1.6.81.1"]}, "T1.6.82.1"->{ Cell[463452, 12314, 57, 1, 46, "Subsection", CellTags->"T1.6.82.1"]}, "T1.6.83.1"->{ Cell[466712, 12407, 59, 1, 46, "Subsection", CellTags->"T1.6.83.1"]}, "T1.6.84.1"->{ Cell[467028, 12421, 61, 1, 46, "Subsection", CellTags->"T1.6.84.1"]}, "T1.6.85.1"->{ Cell[467532, 12441, 61, 1, 46, "Subsection", CellTags->"T1.6.85.1"]}, "T1.6.86.1"->{ Cell[468083, 12462, 57, 1, 46, "Subsection", CellTags->"T1.6.86.1"]}, "T1.6.87.1"->{ Cell[470429, 12538, 59, 1, 46, "Subsection", CellTags->"T1.6.87.1"]}, "T1.6.88.1"->{ Cell[470756, 12553, 57, 1, 46, "Subsection", CellTags->"T1.6.88.1"]}, "T1.6.89.1"->{ Cell[473086, 12626, 59, 1, 46, "Subsection", CellTags->"T1.6.89.1"]}, "T1.6.90.1"->{ Cell[473375, 12640, 57, 1, 46, "Subsection", CellTags->"T1.6.90.1"]}, "T1.6.91.1"->{ Cell[474903, 12693, 59, 1, 46, "Subsection", CellTags->"T1.6.91.1"]}, "T1.6.92.1"->{ Cell[475207, 12707, 57, 1, 46, "Subsection", CellTags->"T1.6.92.1"]}, "T1.6.93.1"->{ Cell[476593, 12756, 59, 1, 46, "Subsection", CellTags->"T1.6.93.1"]}, "T1.6.94.1"->{ Cell[476871, 12770, 57, 1, 46, "Subsection", CellTags->"T1.6.94.1"]}, "T1.6.95.1"->{ Cell[480822, 12888, 59, 1, 46, "Subsection", CellTags->"T1.6.95.1"]}, "T1.6.96.1"->{ Cell[481135, 12902, 61, 1, 46, "Subsection", CellTags->"T1.6.96.1"]}, "T1.6.97.1"->{ Cell[481510, 12918, 61, 1, 46, "Subsection", CellTags->"T1.6.97.1"]}, "T1.6.98.1"->{ Cell[481885, 12934, 58, 1, 46, "Subsection", CellTags->"T1.6.98.1"]}, "T1.6.99.1"->{ Cell[488054, 13112, 60, 1, 46, "Subsection", CellTags->"T1.6.99.1"]}, "T1.6.100.1"->{ Cell[488420, 13129, 62, 1, 46, "Subsection", CellTags->"T1.6.100.1"]}, "T1.6.101.1"->{ Cell[488829, 13146, 62, 1, 46, "Subsection", CellTags->"T1.6.101.1"]}, "T1.6.102.1"->{ Cell[489271, 13165, 62, 1, 46, "Subsection", CellTags->"T1.6.102.1"]}, "T1.6.103.1"->{ Cell[489680, 13182, 62, 1, 46, "Subsection", CellTags->"T1.6.103.1"]}, "T1.6.104.1"->{ Cell[490089, 13199, 62, 1, 46, "Subsection", CellTags->"T1.6.104.1"]}, "T1.6.105.1"->{ Cell[490531, 13218, 59, 1, 46, "Subsection", CellTags->"T1.6.105.1"]}, "T1.6.106.1"->{ Cell[491271, 13243, 61, 1, 46, "Subsection", CellTags->"T1.6.106.1"]}, "T1.6.107.1"->{ Cell[491493, 13255, 59, 1, 46, "Subsection", CellTags->"T1.6.107.1"]}, "T1.6.108.1"->{ Cell[492364, 13285, 61, 1, 46, "Subsection", CellTags->"T1.6.108.1"]}, "T1.6.109.1"->{ Cell[492630, 13299, 59, 1, 46, "Subsection", CellTags->"T1.6.109.1"]}, "T1.6.110.1"->{ Cell[493335, 13323, 61, 1, 46, "Subsection", CellTags->"T1.6.110.1"]}, "T1.6.111.1"->{ Cell[493557, 13335, 59, 1, 46, "Subsection", CellTags->"T1.6.111.1"]}, "T1.6.112.1"->{ Cell[494011, 13352, 61, 1, 46, "Subsection", CellTags->"T1.6.112.1"]}, "T1.6.113.1"->{ Cell[494233, 13364, 59, 1, 46, "Subsection", CellTags->"T1.6.113.1"]}, "T1.6.114.1"->{ Cell[501398, 13554, 61, 1, 46, "Subsection", CellTags->"T1.6.114.1"]}, "T1.6.115.1"->{ Cell[502000, 13575, 61, 1, 46, "Subsection", CellTags->"T1.6.115.1"]}, "T1.6.116.1"->{ Cell[502793, 13612, 61, 1, 46, "Subsection", CellTags->"T1.6.116.1"]}, "T1.6.117.1"->{ Cell[503590, 13649, 62, 1, 46, "Subsection", CellTags->"T1.6.117.1"]}, "T1.6.118.1"->{ Cell[504712, 13676, 62, 1, 46, "Subsection", CellTags->"T1.6.118.1"]}, "T1.6.119.1"->{ Cell[505797, 13702, 62, 1, 46, "Subsection", CellTags->"T1.6.119.1"]}, "T1.6.120.1"->{ Cell[506880, 13728, 61, 1, 46, "Subsection", CellTags->"T1.6.120.1"]}, "T1.6.121.1"->{ Cell[512577, 13846, 60, 1, 46, "Subsection", CellTags->"T1.6.121.1"]}, "T1.6.122.1"->{ Cell[514579, 13902, 61, 1, 46, "Subsection", CellTags->"T1.6.122.1"]}, "T1.6.123.1"->{ Cell[515632, 13933, 60, 1, 46, "Subsection", CellTags->"T1.6.123.1"]}, "T1.6.124.1"->{ Cell[516287, 13954, 58, 1, 46, "Subsection", CellTags->"T1.6.124.1"]}, "T1.7.1"->{ Cell[516934, 13978, 108, 2, 34, "Section", CellTags->"T1.7.1"]}, "T1.7.1.1"->{ Cell[517067, 13984, 56, 1, 46, "Subsection", CellTags->"T1.7.1.1"]}, "T1.7.2.1"->{ Cell[531615, 14381, 50, 1, 46, "Subsection", CellTags->"T1.7.2.1"]}, "T1.7.3.1"->{ Cell[536999, 14506, 54, 1, 46, "Subsection", CellTags->"T1.7.3.1"]}, "T1.7.4.1"->{ Cell[538519, 14542, 59, 1, 46, "Subsection", CellTags->"T1.7.4.1"]}, "T1.8.1"->{ Cell[546052, 14704, 92, 2, 34, "Section", CellTags->"T1.8.1"]}, "T1.9.1"->{ Cell[550051, 14788, 93, 2, 34, "Section", CellTags->"T1.9.1"]}, "T1.9.1.1"->{ Cell[550169, 14794, 54, 1, 46, "Subsection", CellTags->"T1.9.1.1"]}, "T1.10.1"->{ Cell[553872, 14906, 95, 2, 34, "Section", CellTags->"T1.10.1"]}, "T1.11.1"->{ Cell[555790, 14974, 101, 2, 34, "Section", CellTags->"T1.11.1"]} } *) (*CellTagsIndex CellTagsIndex->{ {"T1.1", 560013, 15081}, {"T1.2", 560091, 15084}, {"T1.1.1", 560172, 15087}, {"T1.2.1.1", 560260, 15090}, {"T1.2.1", 560354, 15093}, {"T1.3.1", 560440, 15096}, {"T1.3.1.1", 560529, 15099}, {"T1.3.2.1", 560622, 15102}, {"T1.3.3.1", 560715, 15105}, {"T1.3.4.1", 560808, 15108}, {"T1.3.5.1", 560901, 15111}, {"T1.3.6.1", 560994, 15114}, {"T1.3.7.1", 561087, 15117}, {"T1.3.7.1.1", 561182, 15120}, {"T1.3.7.2.1", 561282, 15123}, {"T1.3.7.3.1", 561382, 15126}, {"T1.3.7.4.1", 561482, 15129}, {"T1.3.7.5.1", 561582, 15132}, {"T1.3.7.6.1", 561682, 15135}, {"T1.3.7.7.1", 561782, 15138}, {"T1.3.7.8.1", 561882, 15141}, {"T1.4.1", 561978, 15144}, {"T1.4.1.1", 562067, 15147}, {"T1.4.2.1", 562161, 15150}, {"T1.4.3.1", 562255, 15153}, {"T1.4.4.1", 562350, 15156}, {"T1.5.1", 562443, 15159}, {"T1.5.1.1", 562532, 15162}, {"T1.5.1.1.1", 562628, 15165}, {"T1.5.2.1", 562727, 15168}, {"T1.5.2.1.1", 562823, 15171}, {"T1.5.3.1", 562922, 15174}, {"T1.5.3.1.1", 563018, 15177}, {"T1.5.3.2.1", 563119, 15180}, {"T1.6.1", 563216, 15183}, {"T1.6.1.1", 563306, 15186}, {"T1.6.2.1", 563400, 15189}, {"T1.6.2.1.1", 563496, 15192}, {"T1.6.2.2.1", 563598, 15195}, {"T1.6.2.3.1", 563700, 15198}, {"T1.6.2.4.1", 563802, 15201}, {"T1.6.3.1", 563902, 15204}, {"T1.6.4.1", 563996, 15207}, {"T1.6.5.1", 564091, 15210}, {"T1.6.6.1", 564185, 15213}, {"T1.6.7.1", 564280, 15216}, {"T1.6.8.1", 564375, 15219}, {"T1.6.9.1", 564470, 15222}, {"T1.6.10.1", 564565, 15225}, {"T1.6.11.1", 564661, 15228}, {"T1.6.12.1", 564757, 15231}, {"T1.6.13.1", 564853, 15234}, {"T1.6.14.1", 564949, 15237}, {"T1.6.15.1", 565045, 15240}, {"T1.6.16.1", 565141, 15243}, {"T1.6.17.1", 565237, 15246}, {"T1.6.18.1", 565333, 15249}, {"T1.6.19.1", 565429, 15252}, {"T1.6.20.1", 565525, 15255}, {"T1.6.21.1", 565621, 15258}, {"T1.6.22.1", 565717, 15261}, {"T1.6.23.1", 565813, 15264}, {"T1.6.24.1", 565909, 15267}, {"T1.6.25.1", 566005, 15270}, {"T1.6.26.1", 566101, 15273}, {"T1.6.27.1", 566197, 15276}, {"T1.6.28.1", 566293, 15279}, {"T1.6.29.1", 566389, 15282}, {"T1.6.30.1", 566485, 15285}, {"T1.6.31.1", 566581, 15288}, {"T1.6.32.1", 566677, 15291}, {"T1.6.33.1", 566773, 15294}, {"T1.6.34.1", 566869, 15297}, {"T1.6.35.1", 566965, 15300}, {"T1.6.36.1", 567061, 15303}, {"T1.6.37.1", 567157, 15306}, {"T1.6.38.1", 567253, 15309}, {"T1.6.39.1", 567349, 15312}, {"T1.6.40.1", 567445, 15315}, {"T1.6.41.1", 567541, 15318}, {"T1.6.42.1", 567637, 15321}, {"T1.6.43.1", 567733, 15324}, {"T1.6.44.1", 567829, 15327}, {"T1.6.45.1", 567925, 15330}, {"T1.6.46.1", 568021, 15333}, {"T1.6.47.1", 568117, 15336}, {"T1.6.48.1", 568213, 15339}, {"T1.6.49.1", 568309, 15342}, {"T1.6.50.1", 568405, 15345}, {"T1.6.51.1", 568501, 15348}, {"T1.6.52.1", 568597, 15351}, {"T1.6.53.1", 568693, 15354}, {"T1.6.54.1", 568790, 15357}, {"T1.6.55.1", 568887, 15360}, {"T1.6.56.1", 568984, 15363}, {"T1.6.57.1", 569081, 15366}, {"T1.6.58.1", 569178, 15369}, {"T1.6.59.1", 569275, 15372}, {"T1.6.60.1", 569372, 15375}, {"T1.6.61.1", 569469, 15378}, {"T1.6.62.1", 569566, 15381}, {"T1.6.63.1", 569663, 15384}, {"T1.6.64.1", 569760, 15387}, {"T1.6.65.1", 569857, 15390}, {"T1.6.66.1", 569954, 15393}, {"T1.6.67.1", 570051, 15396}, {"T1.6.68.1", 570148, 15399}, {"T1.6.69.1", 570245, 15402}, {"T1.6.70.1", 570342, 15405}, {"T1.6.70.1.1", 570441, 15408}, {"T1.6.70.2.1", 570545, 15411}, {"T1.6.71.1", 570647, 15414}, {"T1.6.72.1", 570744, 15417}, {"T1.6.73.1", 570841, 15420}, {"T1.6.74.1", 570938, 15423}, {"T1.6.75.1", 571035, 15426}, {"T1.6.76.1", 571132, 15429}, {"T1.6.77.1", 571229, 15432}, {"T1.6.78.1", 571326, 15435}, {"T1.6.79.1", 571423, 15438}, {"T1.6.80.1", 571520, 15441}, {"T1.6.81.1", 571617, 15444}, {"T1.6.82.1", 571714, 15447}, {"T1.6.83.1", 571811, 15450}, {"T1.6.84.1", 571908, 15453}, {"T1.6.85.1", 572005, 15456}, {"T1.6.86.1", 572102, 15459}, {"T1.6.87.1", 572199, 15462}, {"T1.6.88.1", 572296, 15465}, {"T1.6.89.1", 572393, 15468}, {"T1.6.90.1", 572490, 15471}, {"T1.6.91.1", 572587, 15474}, {"T1.6.92.1", 572684, 15477}, {"T1.6.93.1", 572781, 15480}, {"T1.6.94.1", 572878, 15483}, {"T1.6.95.1", 572975, 15486}, {"T1.6.96.1", 573072, 15489}, {"T1.6.97.1", 573169, 15492}, {"T1.6.98.1", 573266, 15495}, {"T1.6.99.1", 573363, 15498}, {"T1.6.100.1", 573461, 15501}, {"T1.6.101.1", 573560, 15504}, {"T1.6.102.1", 573659, 15507}, {"T1.6.103.1", 573758, 15510}, {"T1.6.104.1", 573857, 15513}, {"T1.6.105.1", 573956, 15516}, {"T1.6.106.1", 574055, 15519}, {"T1.6.107.1", 574154, 15522}, {"T1.6.108.1", 574253, 15525}, {"T1.6.109.1", 574352, 15528}, {"T1.6.110.1", 574451, 15531}, {"T1.6.111.1", 574550, 15534}, {"T1.6.112.1", 574649, 15537}, {"T1.6.113.1", 574748, 15540}, {"T1.6.114.1", 574847, 15543}, {"T1.6.115.1", 574946, 15546}, {"T1.6.116.1", 575045, 15549}, {"T1.6.117.1", 575144, 15552}, {"T1.6.118.1", 575243, 15555}, {"T1.6.119.1", 575342, 15558}, {"T1.6.120.1", 575441, 15561}, {"T1.6.121.1", 575540, 15564}, {"T1.6.122.1", 575639, 15567}, {"T1.6.123.1", 575738, 15570}, {"T1.6.124.1", 575837, 15573}, {"T1.7.1", 575932, 15576}, {"T1.7.1.1", 576023, 15579}, {"T1.7.2.1", 576118, 15582}, {"T1.7.3.1", 576213, 15585}, {"T1.7.4.1", 576308, 15588}, {"T1.8.1", 576401, 15591}, {"T1.9.1", 576489, 15594}, {"T1.9.1.1", 576579, 15597}, {"T1.10.1", 576673, 15600}, {"T1.11.1", 576763, 15603} } *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1731, 51, 72, 2, 107, "Title", CellTags->"T1.1"], Cell[1806, 55, 177, 6, 32, "Text"], Cell[1986, 63, 434, 14, 104, "Text", CellTags->"T1.2"], Cell[2423, 79, 55, 1, 32, "Text"], Cell[2481, 82, 201, 7, 32, "Text"], Cell[CellGroupData[{ Cell[2707, 93, 75, 1, 54, "Section"], Cell[2785, 96, 154, 3, 50, "Text"], Cell[2942, 101, 187, 4, 32, "Text"], Cell[3132, 107, 180, 4, 32, "Text"], Cell[3315, 113, 205, 4, 32, "Text"], Cell[3523, 119, 206, 4, 32, "Text"], Cell[3732, 125, 193, 4, 32, "Text"], Cell[3928, 131, 188, 4, 32, "Text"], Cell[4119, 137, 189, 4, 32, "Text"], Cell[4311, 143, 190, 4, 32, "Text"], Cell[4504, 149, 184, 4, 32, "Text"], Cell[4691, 155, 189, 4, 32, "Text"], Cell[4883, 161, 180, 4, 32, "Text"], Cell[5066, 167, 189, 4, 27, "SmallText"], Cell[5258, 173, 185, 4, 27, "SmallText"], Cell[5446, 179, 186, 4, 27, "SmallText"], Cell[5635, 185, 190, 4, 27, "SmallText"], Cell[5828, 191, 186, 4, 27, "SmallText"], Cell[6017, 197, 186, 4, 27, "SmallText"], Cell[6206, 203, 186, 4, 27, "SmallText"], Cell[6395, 209, 186, 4, 27, "SmallText"], Cell[6584, 215, 198, 4, 32, "Text"], Cell[6785, 221, 228, 5, 32, "Text"], Cell[7016, 228, 226, 5, 32, "Text"], Cell[7245, 235, 640, 18, 36, "Text"], Cell[7888, 255, 657, 18, 36, "Text"], Cell[8548, 275, 191, 4, 32, "Text"], Cell[8742, 281, 195, 4, 32, "Text"], Cell[8940, 287, 194, 4, 27, "SmallText"], Cell[9137, 293, 343, 9, 32, "Text"], Cell[9483, 304, 185, 4, 27, "SmallText"], Cell[9671, 310, 190, 4, 32, "Text"], Cell[9864, 316, 200, 4, 27, "SmallText"], Cell[10067, 322, 200, 4, 27, "SmallText"], Cell[10270, 328, 235, 5, 32, "Text"], Cell[10508, 335, 186, 4, 32, "Text"], Cell[10697, 341, 188, 4, 32, "Text"], Cell[10888, 347, 582, 16, 31, "SmallText"], Cell[11473, 365, 582, 16, 31, "SmallText"], Cell[12058, 383, 582, 16, 31, "SmallText"], Cell[12643, 401, 582, 16, 31, "SmallText"], Cell[13228, 419, 188, 4, 32, "Text"], Cell[13419, 425, 606, 16, 39, "Text"], Cell[14028, 443, 188, 4, 32, "Text"], Cell[14219, 449, 606, 16, 39, "Text"], Cell[14828, 467, 606, 16, 39, "Text"], Cell[15437, 485, 606, 16, 39, "Text"], Cell[16046, 503, 186, 4, 32, "Text"], Cell[16235, 509, 189, 4, 32, "Text"], Cell[16427, 515, 187, 4, 32, "Text"], Cell[16617, 521, 187, 4, 32, "Text"], Cell[16807, 527, 187, 4, 32, "Text"], Cell[16997, 533, 198, 4, 32, "Text"], Cell[17198, 539, 189, 4, 32, "Text"], Cell[17390, 545, 187, 4, 32, "Text"], Cell[17580, 551, 189, 4, 32, "Text"], Cell[17772, 557, 187, 4, 32, "Text"], Cell[17962, 563, 189, 4, 32, "Text"], Cell[18154, 569, 189, 4, 32, "Text"], Cell[18346, 575, 187, 4, 32, "Text"], Cell[18536, 581, 189, 4, 32, "Text"], Cell[18728, 587, 187, 4, 32, "Text"], Cell[18918, 593, 189, 4, 32, "Text"], Cell[19110, 599, 187, 4, 32, "Text"], Cell[19300, 605, 189, 4, 32, "Text"], Cell[19492, 611, 187, 4, 32, "Text"], Cell[19682, 617, 189, 4, 32, "Text"], Cell[19874, 623, 187, 4, 32, "Text"], Cell[20064, 629, 189, 4, 32, "Text"], Cell[20256, 635, 187, 4, 32, "Text"], Cell[20446, 641, 189, 4, 32, "Text"], Cell[20638, 647, 191, 4, 32, "Text"], Cell[20832, 653, 187, 4, 32, "Text"], Cell[21022, 659, 189, 4, 32, "Text"], Cell[21214, 665, 187, 4, 32, "Text"], Cell[21404, 671, 189, 4, 32, "Text"], Cell[21596, 677, 191, 4, 32, "Text"], Cell[21790, 683, 191, 4, 32, "Text"], Cell[21984, 689, 191, 4, 32, "Text"], Cell[22178, 695, 187, 4, 32, "Text"], Cell[22368, 701, 189, 4, 30, "Text"], Cell[22560, 707, 198, 4, 30, "Text"], Cell[22761, 713, 187, 4, 30, "Text"], Cell[22951, 719, 189, 4, 30, "Text"], Cell[23143, 725, 191, 4, 30, "Text"], Cell[23337, 731, 187, 4, 30, "Text"], Cell[23527, 737, 189, 4, 30, "Text"], Cell[23719, 743, 191, 4, 30, "Text"], Cell[23913, 749, 187, 4, 30, "Text"], Cell[24103, 755, 189, 4, 30, "Text"], Cell[24295, 761, 187, 4, 30, "Text"], Cell[24485, 767, 189, 4, 30, "Text"], Cell[24677, 773, 191, 4, 30, "Text"], Cell[24871, 779, 191, 4, 30, "Text"], Cell[25065, 785, 187, 4, 30, "Text"], Cell[25255, 791, 189, 4, 30, "Text"], Cell[25447, 797, 187, 4, 30, "Text"], Cell[25637, 803, 189, 4, 30, "Text"], Cell[25829, 809, 187, 4, 30, "Text"], Cell[26019, 815, 189, 4, 30, "Text"], Cell[26211, 821, 191, 4, 30, "Text"], Cell[26405, 827, 191, 4, 30, "Text"], Cell[26599, 833, 187, 4, 30, "Text"], Cell[26789, 839, 189, 4, 30, "Text"], Cell[26981, 845, 191, 4, 30, "Text"], Cell[27175, 851, 191, 4, 30, "Text"], Cell[27369, 857, 187, 4, 30, "Text"], Cell[27559, 863, 189, 4, 30, "Text"], Cell[27751, 869, 187, 4, 30, "Text"], Cell[27941, 875, 188, 4, 26, "SmallText"], Cell[28132, 881, 188, 4, 26, "SmallText"], Cell[28323, 887, 189, 4, 30, "Text"], Cell[28515, 893, 187, 4, 30, "Text"], Cell[28705, 899, 189, 4, 30, "Text"], Cell[28897, 905, 187, 4, 30, "Text"], Cell[29087, 911, 190, 4, 30, "Text"], Cell[29280, 917, 190, 4, 30, "Text"], Cell[29473, 923, 190, 4, 30, "Text"], Cell[29666, 929, 190, 4, 30, "Text"], Cell[29859, 935, 187, 4, 30, "Text"], Cell[30049, 941, 187, 4, 30, "Text"], Cell[30239, 947, 189, 4, 30, "Text"], Cell[30431, 953, 187, 4, 30, "Text"], Cell[30621, 959, 189, 4, 30, "Text"], Cell[30813, 965, 191, 4, 30, "Text"], Cell[31007, 971, 191, 4, 30, "Text"], Cell[31201, 977, 187, 4, 30, "Text"], Cell[31391, 983, 189, 4, 30, "Text"], Cell[31583, 989, 187, 4, 30, "Text"], Cell[31773, 995, 189, 4, 30, "Text"], Cell[31965, 1001, 187, 4, 30, "Text"], Cell[32155, 1007, 189, 4, 30, "Text"], Cell[32347, 1013, 187, 4, 30, "Text"], Cell[32537, 1019, 189, 4, 30, "Text"], Cell[32729, 1025, 187, 4, 30, "Text"], Cell[32919, 1031, 189, 4, 30, "Text"], Cell[33111, 1037, 191, 4, 30, "Text"], Cell[33305, 1043, 191, 4, 30, "Text"], Cell[33499, 1049, 188, 4, 30, "Text"], Cell[33690, 1055, 190, 4, 30, "Text"], Cell[33883, 1061, 192, 4, 30, "Text"], Cell[34078, 1067, 192, 4, 30, "Text"], Cell[34273, 1073, 192, 4, 30, "Text"], Cell[34468, 1079, 192, 4, 30, "Text"], Cell[34663, 1085, 192, 4, 30, "Text"], Cell[34858, 1091, 189, 4, 30, "Text"], Cell[35050, 1097, 191, 4, 30, "Text"], Cell[35244, 1103, 189, 4, 30, "Text"], Cell[35436, 1109, 191, 4, 30, "Text"], Cell[35630, 1115, 189, 4, 30, "Text"], Cell[35822, 1121, 191, 4, 30, "Text"], Cell[36016, 1127, 189, 4, 30, "Text"], Cell[36208, 1133, 191, 4, 30, "Text"], Cell[36402, 1139, 189, 4, 30, "Text"], Cell[36594, 1145, 191, 4, 30, "Text"], Cell[36788, 1151, 191, 4, 30, "Text"], Cell[36982, 1157, 191, 4, 30, "Text"], Cell[37176, 1163, 191, 4, 30, "Text"], Cell[37370, 1169, 191, 4, 30, "Text"], Cell[37564, 1175, 191, 4, 30, "Text"], Cell[37758, 1181, 191, 4, 30, "Text"], Cell[37952, 1187, 190, 4, 30, "Text"], Cell[38145, 1193, 191, 4, 30, "Text"], Cell[38339, 1199, 190, 4, 30, "Text"], Cell[38532, 1205, 188, 4, 30, "Text"], Cell[38723, 1211, 202, 4, 30, "Text"], Cell[38928, 1217, 186, 4, 30, "Text"], Cell[39117, 1223, 180, 4, 30, "Text"], Cell[39300, 1229, 184, 4, 30, "Text"], Cell[39487, 1235, 189, 4, 30, "Text"], Cell[39679, 1241, 186, 4, 30, "Text"], Cell[39868, 1247, 187, 4, 30, "Text"], Cell[40058, 1253, 190, 4, 30, "Text"], Cell[40251, 1259, 178, 4, 30, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[40466, 1268, 93, 2, 34, "Section", CellTags->"T1.1.1"], Cell[40562, 1272, 342, 10, 56, "SmallText"], Cell[40907, 1284, 118, 3, 30, "Text"], Cell[41028, 1289, 1662, 41, 77, "Text"], Cell[42693, 1332, 222, 5, 80, "Text"], Cell[42918, 1339, 51, 1, 26, "Input"], Cell[42972, 1342, 61, 1, 26, "Input"], Cell[43036, 1345, 107, 3, 30, "Text"], Cell[43146, 1350, 139, 4, 41, "Input"], Cell[43288, 1356, 220, 6, 41, "SmallText"], Cell[43511, 1364, 244, 5, 72, "Input"], Cell[CellGroupData[{ Cell[43780, 1373, 78, 1, 40, "Subsubsection", CellTags->"T1.2.1.1"], Cell[43861, 1376, 512, 11, 97, "Text"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[44422, 1393, 86, 2, 34, "Section", CellTags->"T1.2.1"], Cell[44511, 1397, 61, 0, 25, "Input"], Cell[44575, 1399, 78, 1, 41, "Input"], Cell[44656, 1402, 263, 4, 72, "Input"], Cell[44922, 1408, 637, 9, 164, "Input"], Cell[45562, 1419, 165, 3, 41, "Input"], Cell[45730, 1424, 131, 3, 41, "Input"], Cell[45864, 1429, 143, 3, 41, "Input"], Cell[46010, 1434, 143, 3, 41, "Input"], Cell[46156, 1439, 153, 3, 41, "Input"], Cell[46312, 1444, 134, 3, 41, "Input"], Cell[46449, 1449, 311, 6, 87, "Input"], Cell[46763, 1457, 219, 4, 56, "Input"], Cell[46985, 1463, 182, 3, 41, "Input"], Cell[47170, 1468, 178, 3, 41, "Input"], Cell[47351, 1473, 203, 4, 56, "Input"], Cell[47557, 1479, 183, 3, 41, "Input"], Cell[47743, 1484, 174, 3, 41, "Input"], Cell[47920, 1489, 157, 3, 41, "Input"], Cell[48080, 1494, 157, 3, 41, "Input"], Cell[48240, 1499, 157, 3, 41, "Input"], Cell[48400, 1504, 157, 3, 41, "Input"], Cell[48560, 1509, 157, 3, 43, "Input"], Cell[48720, 1514, 457, 7, 123, "Input"], Cell[49180, 1523, 188, 3, 59, "Input"], Cell[49371, 1528, 188, 3, 59, "Input"], Cell[49562, 1533, 152, 3, 43, "Input"], Cell[49717, 1538, 256, 4, 75, "Input"], Cell[49976, 1544, 61, 1, 27, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[50074, 1550, 112, 2, 34, "Section", CellTags->"T1.3.1"], Cell[50189, 1554, 775, 23, 50, "Text"], Cell[50967, 1579, 58, 1, 27, "Input"], Cell[51028, 1582, 73, 0, 32, "Text"], Cell[51104, 1584, 62, 1, 27, "Input"], Cell[51169, 1587, 115, 3, 32, "Text"], Cell[51287, 1592, 59, 1, 27, "Input"], Cell[51349, 1595, 754, 24, 50, "Text"], Cell[CellGroupData[{ Cell[52128, 1623, 63, 1, 45, "Subsection", CellTags->"T1.3.1.1"], Cell[52194, 1626, 61, 1, 27, "Input"], Cell[52258, 1629, 261, 5, 72, "Input"], Cell[52522, 1636, 261, 5, 72, "Input"], Cell[52786, 1643, 169, 3, 41, "Input"], Cell[52958, 1648, 115, 3, 30, "Text"], Cell[53076, 1653, 213, 4, 56, "Input"], Cell[53292, 1659, 192, 3, 41, "Input"], Cell[53487, 1664, 216, 4, 41, "Input"], Cell[53706, 1670, 238, 4, 56, "Input"], Cell[53947, 1676, 145, 2, 41, "Input"], Cell[54095, 1680, 162, 2, 41, "Input"], Cell[54260, 1684, 194, 4, 56, "Input"], Cell[54457, 1690, 179, 3, 56, "Input"], Cell[54639, 1695, 513, 13, 172, "Input"], Cell[55155, 1710, 585, 10, 240, "Input"], Cell[55743, 1722, 1014, 21, 256, "Input"], Cell[56760, 1745, 539, 9, 118, "Input"], Cell[57302, 1756, 642, 11, 148, "Input"], Cell[57947, 1769, 547, 9, 133, "Input"], Cell[58497, 1780, 654, 12, 133, "Input"], Cell[59154, 1794, 202, 3, 26, "Input"], Cell[59359, 1799, 684, 11, 133, "Input"], Cell[60046, 1812, 607, 11, 118, "Input"], Cell[60656, 1825, 387, 6, 87, "Input"], Cell[61046, 1833, 607, 11, 118, "Input"], Cell[61656, 1846, 172, 3, 26, "Input"], Cell[61831, 1851, 387, 6, 87, "Input"], Cell[62221, 1859, 493, 8, 118, "Input"], Cell[62717, 1869, 135, 2, 26, "Input"], Cell[62855, 1873, 489, 8, 118, "Input"], Cell[63347, 1883, 108, 2, 26, "Input"], Cell[63458, 1887, 107, 3, 47, "Text"], Cell[63568, 1892, 571, 9, 118, "Input"], Cell[64142, 1903, 571, 9, 118, "Input"], Cell[64716, 1914, 550, 9, 133, "Input"], Cell[65269, 1925, 659, 12, 133, "Input"], Cell[65931, 1939, 689, 11, 133, "Input"], Cell[66623, 1952, 612, 11, 118, "Input"], Cell[67238, 1965, 389, 6, 87, "Input"], Cell[67630, 1973, 496, 8, 118, "Input"], Cell[68129, 1983, 492, 8, 118, "Input"], Cell[68624, 1993, 568, 9, 118, "Input"], Cell[69195, 2004, 568, 9, 118, "Input"], Cell[69766, 2015, 547, 9, 133, "Input"], Cell[70316, 2026, 654, 12, 133, "Input"], Cell[70973, 2040, 684, 11, 133, "Input"], Cell[71660, 2053, 607, 11, 118, "Input"], Cell[72270, 2066, 387, 6, 87, "Input"], Cell[72660, 2074, 493, 8, 118, "Input"], Cell[73156, 2084, 489, 8, 118, "Input"], Cell[73648, 2094, 416, 6, 87, "Input"], Cell[74067, 2102, 381, 7, 102, "Input"], Cell[74451, 2111, 111, 2, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[74599, 2118, 58, 1, 46, "Subsection", CellTags->"T1.3.2.1"], Cell[74660, 2121, 4315, 72, 1025, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[79012, 2198, 59, 1, 46, "Subsection", CellTags->"T1.3.3.1"], Cell[79074, 2201, 494, 9, 134, "Input"], Cell[79571, 2212, 494, 9, 134, "Input"], Cell[80068, 2223, 494, 9, 134, "Input"], Cell[80565, 2234, 494, 9, 134, "Input"], Cell[81062, 2245, 494, 9, 134, "Input"], Cell[81559, 2256, 494, 9, 134, "Input"], Cell[82056, 2267, 494, 9, 134, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[82587, 2281, 60, 1, 46, "Subsection", CellTags->"T1.3.4.1"], Cell[82650, 2284, 755, 18, 133, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[83442, 2307, 54, 1, 46, "Subsection", CellTags->"T1.3.5.1"], Cell[83499, 2310, 170, 3, 56, "Input"], Cell[83672, 2315, 1902, 34, 363, "Input"], Cell[85577, 2351, 185, 3, 56, "Input"], Cell[85765, 2356, 306, 9, 28, "Text"], Cell[86074, 2367, 1923, 33, 388, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[88034, 2405, 59, 1, 46, "Subsection", CellTags->"T1.3.6.1"], Cell[88096, 2408, 460, 8, 102, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[88593, 2421, 50, 1, 46, "Subsection", CellTags->"T1.3.7.1"], Cell[88646, 2424, 84, 1, 26, "Input"], Cell[CellGroupData[{ Cell[88755, 2429, 57, 1, 40, "Subsubsection", CellTags->"T1.3.7.1.1"], Cell[88815, 2432, 779, 28, 35, "Text"], Cell[89597, 2462, 1819, 32, 394, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[91453, 2499, 53, 1, 40, "Subsubsection", CellTags->"T1.3.7.2.1"], Cell[91509, 2502, 72, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[91618, 2508, 54, 1, 40, "Subsubsection", CellTags->"T1.3.7.3.1"], Cell[91675, 2511, 52, 1, 26, "Input"], Cell[91730, 2514, 73, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[91840, 2520, 58, 1, 40, "Subsubsection", CellTags->"T1.3.7.4.1"], Cell[91901, 2523, 78, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[92016, 2529, 54, 1, 40, "Subsubsection", CellTags->"T1.3.7.5.1"], Cell[92073, 2532, 791, 13, 256, "Input"], Cell[92867, 2547, 1379, 19, 286, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[94283, 2571, 54, 1, 40, "Subsubsection", CellTags->"T1.3.7.6.1"], Cell[94340, 2574, 271, 10, 145, "Input"], Cell[94614, 2586, 72, 1, 26, "Input"], Cell[94689, 2589, 74, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[94800, 2595, 54, 1, 40, "Subsubsection", CellTags->"T1.3.7.7.1"], Cell[94857, 2598, 574, 14, 72, "Input"], Cell[95434, 2614, 66, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[95537, 2620, 54, 1, 40, "Subsubsection", CellTags->"T1.3.7.8.1"], Cell[95594, 2623, 215, 6, 26, "Input"] }, Closed]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[95870, 2636, 104, 2, 34, "Section", CellTags->"T1.4.1"], Cell[95977, 2640, 574, 11, 91, "Input"], Cell[96554, 2653, 959, 17, 186, "Input"], Cell[97516, 2672, 136, 4, 30, "Text"], Cell[97655, 2678, 159, 3, 26, "Input"], Cell[97817, 2683, 61, 1, 26, "Input"], Cell[CellGroupData[{ Cell[97903, 2688, 116, 3, 46, "Subsection", CellTags->"T1.4.1.1"], Cell[98022, 2693, 213, 6, 26, "Input"], Cell[98238, 2701, 72, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[98347, 2707, 114, 3, 46, "Subsection", CellTags->"T1.4.2.1"], Cell[98464, 2712, 113, 5, 30, "Text"], Cell[98580, 2719, 1952, 52, 58, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[100569, 2776, 205, 6, 46, "Subsection", CellTags->"T1.4.3.1"], Cell[100777, 2784, 2379, 57, 73, "Input"], Cell[103159, 2843, 157, 4, 26, "Input"], Cell[103319, 2849, 1177, 25, 74, "Input"], Cell[104499, 2876, 772, 19, 58, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[105308, 2900, 223, 6, 56, "Subsection", CellTags->"T1.4.4.1"], Cell[105534, 2908, 3158, 73, 138, "Input"], Cell[108695, 2983, 2826, 70, 120, "Input"], Cell[111524, 3055, 2826, 70, 120, "Input"], Cell[114353, 3127, 2826, 70, 120, "Input"], Cell[117182, 3199, 157, 4, 26, "Input"], Cell[117342, 3205, 157, 4, 26, "Input"], Cell[117502, 3211, 139, 4, 26, "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[117690, 3221, 97, 2, 34, "Section", CellTags->"T1.5.1"], Cell[CellGroupData[{ Cell[117812, 3227, 65, 1, 46, "Subsection", CellTags->"T1.5.1.1"], Cell[117880, 3230, 131, 3, 47, "Text"], Cell[118014, 3235, 67, 0, 30, "Text"], Cell[118084, 3237, 159, 5, 30, "Text"], Cell[118246, 3244, 1155, 19, 136, "Input"], Cell[119404, 3265, 1133, 19, 136, "Input"], Cell[120540, 3286, 100, 2, 26, "Input"], Cell[120643, 3290, 88, 1, 26, "Input"], Cell[120734, 3293, 119, 2, 26, "Input"], Cell[120856, 3297, 108, 2, 26, "Input"], Cell[120967, 3301, 88, 1, 26, "Input"], Cell[121058, 3304, 129, 2, 41, "Input"], Cell[121190, 3308, 2892, 85, 154, "Input"], Cell[124085, 3395, 1732, 36, 133, "Input"], Cell[125820, 3433, 537, 12, 56, "Input"], Cell[126360, 3447, 76, 0, 30, "Text"], Cell[126439, 3449, 202, 6, 26, "Input"], Cell[126644, 3457, 152, 4, 26, "Input"], Cell[126799, 3463, 9841, 176, 614, "Input"], Cell[136643, 3641, 9224, 164, 612, "Input"], Cell[145870, 3807, 12142, 217, 722, "Input"], Cell[158015, 4026, 11119, 200, 624, "Input"], Cell[169137, 4228, 10440, 187, 677, "Input"], Cell[179580, 4417, 69, 1, 26, "Input"], Cell[179652, 4420, 804, 19, 87, "Input"], Cell[180459, 4441, 746, 18, 56, "Input"], Cell[181208, 4461, 746, 18, 56, "Input"], Cell[CellGroupData[{ Cell[181979, 4483, 62, 1, 40, "Subsubsection", CellTags->"T1.5.1.1.1"], Cell[182044, 4486, 2621, 58, 198, "Input"], Cell[184668, 4546, 150, 2, 26, "Input"], Cell[184821, 4550, 142, 2, 26, "Input"], Cell[184966, 4554, 152, 2, 41, "Input"], Cell[185121, 4558, 193, 4, 26, "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[185363, 4568, 69, 1, 46, "Subsection", CellTags->"T1.5.2.1"], Cell[185435, 4571, 1297, 24, 232, "Input"], Cell[CellGroupData[{ Cell[186757, 4599, 53, 1, 40, "Subsubsection", CellTags->"T1.5.2.1.1"], Cell[186813, 4602, 132, 2, 41, "Input"], Cell[186948, 4606, 145, 2, 41, "Input"], Cell[187096, 4610, 117, 2, 26, "Input"], Cell[187216, 4614, 251, 9, 30, "Text"], Cell[187470, 4625, 20, 0, 30, "Text"], Cell[187493, 4627, 1288, 27, 124, "Input"], Cell[188784, 4656, 20, 0, 30, "Text"], Cell[188807, 4658, 726, 12, 91, "Input"], Cell[189536, 4672, 20, 0, 30, "Text"], Cell[189559, 4674, 506, 9, 69, "Input"], Cell[190068, 4685, 20, 0, 30, "Text"], Cell[190091, 4687, 478, 8, 149, "Input"], Cell[190572, 4697, 20, 0, 30, "Text"], Cell[190595, 4699, 715, 12, 151, "Input"], Cell[191313, 4713, 20, 0, 30, "Text"], Cell[191336, 4715, 1071, 22, 105, "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[192456, 4743, 60, 1, 46, "Subsection", CellTags->"T1.5.3.1"], Cell[192519, 4746, 174, 3, 47, "Text"], Cell[192696, 4751, 139, 3, 47, "Text"], Cell[CellGroupData[{ Cell[192860, 4758, 68, 1, 40, "Subsubsection", CellTags->"T1.5.3.1.1"], Cell[192931, 4761, 342, 6, 88, "Input"], Cell[193276, 4769, 727, 13, 254, "Input"], Cell[194006, 4784, 1776, 32, 396, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[195819, 4821, 68, 1, 40, "Subsubsection", CellTags->"T1.5.3.2.1"], Cell[195890, 4824, 279, 5, 88, "Input"], Cell[196172, 4831, 185, 3, 41, "Input"], Cell[196360, 4836, 1800, 35, 412, "Input"] }, Closed]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[198221, 4878, 140, 2, 56, "Section", CellTags->"T1.6.1"], Cell[198364, 4882, 266, 7, 47, "Text"], Cell[CellGroupData[{ Cell[198655, 4893, 56, 1, 46, "Subsection", CellTags->"T1.6.1.1"], Cell[198714, 4896, 77, 4, 30, "Text"], Cell[198794, 4902, 7362, 170, 78, "Input"], Cell[206159, 5074, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[206258, 5080, 58, 1, 46, "Subsection", CellTags->"T1.6.2.1"], Cell[206319, 5083, 81, 1, 26, "Input"], Cell[CellGroupData[{ Cell[206425, 5088, 131, 5, 40, "Subsubsection", CellTags->"T1.6.2.1.1"], Cell[206559, 5095, 1082, 28, 55, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[207678, 5128, 131, 5, 40, "Subsubsection", CellTags->"T1.6.2.2.1"], Cell[207812, 5135, 1163, 30, 55, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[209012, 5170, 131, 5, 40, "Subsubsection", CellTags->"T1.6.2.3.1"], Cell[209146, 5177, 1163, 30, 55, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[210346, 5212, 131, 5, 40, "Subsubsection", CellTags->"T1.6.2.4.1"], Cell[210480, 5219, 1163, 30, 55, "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[211692, 5255, 58, 1, 46, "Subsection", CellTags->"T1.6.3.1"], Cell[211753, 5258, 73, 1, 26, "Input"], Cell[211829, 5261, 132, 2, 28, "Text"], Cell[211964, 5265, 3415, 89, 29, "Input"], Cell[215382, 5356, 66, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[215485, 5362, 159, 5, 46, "Subsection", CellTags->"T1.6.4.1"], Cell[215647, 5369, 50, 1, 26, "Input"], Cell[215700, 5372, 393, 9, 41, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[216130, 5386, 58, 1, 46, "Subsection", CellTags->"T1.6.5.1"], Cell[216191, 5389, 73, 1, 26, "Input"], Cell[216267, 5392, 132, 2, 28, "Text"], Cell[216402, 5396, 3415, 89, 29, "Input"], Cell[219820, 5487, 66, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[219923, 5493, 159, 5, 46, "Subsection", CellTags->"T1.6.6.1"], Cell[220085, 5500, 50, 1, 26, "Input"], Cell[220138, 5503, 393, 9, 41, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[220568, 5517, 159, 5, 46, "Subsection", CellTags->"T1.6.7.1"], Cell[220730, 5524, 62, 1, 26, "Input"], Cell[220795, 5527, 127, 3, 26, "Input"], Cell[220925, 5532, 393, 9, 41, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[221355, 5546, 159, 5, 46, "Subsection", CellTags->"T1.6.8.1"], Cell[221517, 5553, 62, 1, 26, "Input"], Cell[221582, 5556, 127, 3, 26, "Input"], Cell[221712, 5561, 393, 9, 41, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[222142, 5575, 56, 1, 46, "Subsection", CellTags->"T1.6.9.1"], Cell[222201, 5578, 77, 4, 30, "Text"], Cell[222281, 5584, 6608, 152, 94, "Input"], Cell[228892, 5738, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[228991, 5744, 59, 1, 46, "Subsection", CellTags->"T1.6.10.1"], Cell[229053, 5747, 79, 1, 26, "Input"], Cell[229135, 5750, 1078, 28, 52, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[230250, 5783, 57, 1, 46, "Subsection", CellTags->"T1.6.11.1"], Cell[230310, 5786, 454, 20, 30, "Text"], Cell[230767, 5808, 3684, 95, 44, "Input"], Cell[234454, 5905, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[234553, 5911, 57, 1, 46, "Subsection", CellTags->"T1.6.12.1"], Cell[234613, 5914, 454, 20, 30, "Text"], Cell[235070, 5936, 3684, 95, 44, "Input"], Cell[238757, 6033, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[238856, 6039, 57, 1, 46, "Subsection", CellTags->"T1.6.13.1"], Cell[238916, 6042, 7313, 170, 81, "Input"], Cell[246232, 6214, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[246331, 6220, 68, 1, 46, "Subsection", CellTags->"T1.6.14.1"], Cell[246402, 6223, 201, 4, 41, "Input"], Cell[246606, 6229, 101, 2, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[246744, 6236, 59, 1, 46, "Subsection", CellTags->"T1.6.15.1"], Cell[246806, 6239, 22655, 536, 7132, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[269498, 6780, 57, 1, 46, "Subsection", CellTags->"T1.6.16.1"], Cell[269558, 6783, 77, 4, 30, "Text"], Cell[269638, 6789, 3791, 96, 66, "Input"], Cell[273432, 6887, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[273531, 6893, 59, 1, 46, "Subsection", CellTags->"T1.6.17.1"], Cell[273593, 6896, 38, 1, 26, "Input"], Cell[273634, 6899, 79, 1, 26, "Input"], Cell[273716, 6902, 397, 10, 26, "Input"], Cell[274116, 6914, 57, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[274210, 6920, 57, 1, 46, "Subsection", CellTags->"T1.6.18.1"], Cell[274270, 6923, 77, 4, 30, "Text"], Cell[274350, 6929, 5270, 131, 81, "Input"], Cell[279623, 7062, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[279722, 7068, 59, 1, 46, "Subsection", CellTags->"T1.6.19.1"], Cell[279784, 7071, 97, 2, 26, "Input"], Cell[279884, 7075, 397, 10, 26, "Input"], Cell[280284, 7087, 57, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[280378, 7093, 59, 1, 46, "Subsection", CellTags->"T1.6.20.1"], Cell[280440, 7096, 131, 3, 26, "Input"], Cell[280574, 7101, 397, 10, 26, "Input"], Cell[280974, 7113, 57, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[281068, 7119, 57, 1, 46, "Subsection", CellTags->"T1.6.21.1"], Cell[281128, 7122, 77, 4, 30, "Text"], Cell[281208, 7128, 3179, 83, 48, "Input"], Cell[284390, 7213, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[284489, 7219, 59, 1, 46, "Subsection", CellTags->"T1.6.22.1"], Cell[284551, 7222, 79, 1, 26, "Input"], Cell[284633, 7225, 369, 9, 26, "Input"], Cell[285005, 7236, 57, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[285099, 7242, 57, 1, 46, "Subsection", CellTags->"T1.6.23.1"], Cell[285159, 7245, 77, 4, 30, "Text"], Cell[285239, 7251, 3892, 100, 48, "Input"], Cell[289134, 7353, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[289233, 7359, 59, 1, 46, "Subsection", CellTags->"T1.6.24.1"], Cell[289295, 7362, 79, 1, 26, "Input"], Cell[289377, 7365, 393, 10, 26, "Input"], Cell[289773, 7377, 57, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[289867, 7383, 57, 1, 46, "Subsection", CellTags->"T1.6.25.1"], Cell[289927, 7386, 77, 4, 30, "Text"], Cell[290007, 7392, 3445, 89, 48, "Input"], Cell[293455, 7483, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[293554, 7489, 59, 1, 46, "Subsection", CellTags->"T1.6.26.1"], Cell[293616, 7492, 79, 1, 26, "Input"], Cell[293698, 7495, 395, 10, 26, "Input"], Cell[294096, 7507, 57, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[294190, 7513, 57, 1, 46, "Subsection", CellTags->"T1.6.27.1"], Cell[294250, 7516, 169, 7, 30, "Text"], Cell[294422, 7525, 4987, 124, 85, "Input"], Cell[299412, 7651, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[299511, 7657, 59, 1, 46, "Subsection", CellTags->"T1.6.28.1"], Cell[299573, 7660, 46, 1, 26, "Input"], Cell[299622, 7663, 801, 17, 78, "Input"], Cell[300426, 7682, 50, 0, 30, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[300513, 7687, 58, 1, 46, "Subsection", CellTags->"T1.6.29.1"], Cell[300574, 7690, 77, 4, 30, "Text"], Cell[300654, 7696, 3179, 83, 48, "Input"], Cell[303836, 7781, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[303935, 7787, 59, 1, 46, "Subsection", CellTags->"T1.6.30.1"], Cell[303997, 7790, 79, 1, 26, "Input"], Cell[304079, 7793, 376, 9, 27, "Input"], Cell[304458, 7804, 69, 1, 27, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[304564, 7810, 58, 1, 46, "Subsection", CellTags->"T1.6.31.1"], Cell[304625, 7813, 292, 14, 30, "Text"], Cell[304920, 7829, 2494, 68, 29, "Input"], Cell[307417, 7899, 62, 1, 26, "Input"], Cell[307482, 7902, 2268, 66, 48, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[309787, 7973, 59, 1, 46, "Subsection", CellTags->"T1.6.32.1"], Cell[309849, 7976, 291, 14, 30, "Text"], Cell[310143, 7992, 46, 1, 26, "Input"], Cell[310192, 7995, 653, 18, 26, "Input"], Cell[310848, 8015, 50, 0, 30, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[310935, 8020, 61, 1, 46, "Subsection", CellTags->"T1.6.33.1"], Cell[310999, 8023, 291, 14, 30, "Text"], Cell[311293, 8039, 84, 1, 26, "Input"], Cell[311380, 8042, 659, 18, 26, "Input"], Cell[312042, 8062, 50, 0, 30, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[312129, 8067, 58, 1, 46, "Subsection", CellTags->"T1.6.34.1"], Cell[312190, 8070, 386, 17, 47, "Text"], Cell[312579, 8089, 5063, 127, 82, "Input"], Cell[317645, 8218, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[317744, 8224, 59, 1, 46, "Subsection", CellTags->"T1.6.35.1"], Cell[317806, 8227, 97, 2, 26, "Input"], Cell[317906, 8231, 985, 26, 43, "Input"], Cell[318894, 8259, 50, 0, 30, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[318981, 8264, 58, 1, 46, "Subsection", CellTags->"T1.6.36.1"], Cell[319042, 8267, 201, 7, 47, "Text"], Cell[319246, 8276, 6350, 147, 65, "Input"], Cell[325599, 8425, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[325698, 8431, 59, 1, 46, "Subsection", CellTags->"T1.6.37.1"], Cell[325760, 8434, 170, 7, 30, "Text"], Cell[325933, 8443, 61, 1, 26, "Input"], Cell[325997, 8446, 561, 14, 41, "Input"], Cell[326561, 8462, 57, 1, 26, "Input"], Cell[326621, 8465, 641, 16, 56, "Input"], Cell[327265, 8483, 106, 5, 80, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[327408, 8493, 61, 1, 46, "Subsection", CellTags->"T1.6.38.1"], Cell[327472, 8496, 103, 2, 26, "Input"], Cell[327578, 8500, 425, 11, 26, "Input"], Cell[328006, 8513, 50, 1, 26, "Input"], Cell[328059, 8516, 76, 1, 26, "Input"], Cell[328138, 8519, 52, 1, 26, "Input"], Cell[328193, 8522, 131, 3, 26, "Input"], Cell[328327, 8527, 812, 18, 43, "Input"], Cell[329142, 8547, 50, 0, 30, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[329229, 8552, 61, 1, 46, "Subsection", CellTags->"T1.6.39.1"], Cell[329293, 8555, 103, 2, 26, "Input"], Cell[329399, 8559, 66, 1, 26, "Input"], Cell[329468, 8562, 52, 1, 26, "Input"], Cell[329523, 8565, 131, 3, 26, "Input"], Cell[329657, 8570, 576, 13, 43, "Input"], Cell[330236, 8585, 50, 0, 30, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[330323, 8590, 61, 1, 46, "Subsection", CellTags->"T1.6.40.1"], Cell[330387, 8593, 148, 3, 26, "Input"], Cell[330538, 8598, 131, 3, 26, "Input"], Cell[330672, 8603, 417, 10, 26, "Input"], Cell[331092, 8615, 50, 0, 30, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[331179, 8620, 58, 1, 46, "Subsection", CellTags->"T1.6.41.1"], Cell[331240, 8623, 77, 4, 30, "Text"], Cell[331320, 8629, 4850, 122, 83, "Input"], Cell[336173, 8753, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[336272, 8759, 59, 1, 46, "Subsection", CellTags->"T1.6.42.1"], Cell[336334, 8762, 158, 3, 26, "Input"], Cell[336495, 8767, 454, 11, 41, "Input"], Cell[336952, 8780, 57, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[337046, 8786, 68, 1, 46, "Subsection", CellTags->"T1.6.43.1"], Cell[337117, 8789, 111, 3, 30, "Text"], Cell[337231, 8794, 77, 4, 30, "Text"], Cell[337311, 8800, 5393, 138, 83, "Input"], Cell[342707, 8940, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[342806, 8946, 57, 1, 46, "Subsection", CellTags->"T1.6.44.1"], Cell[342866, 8949, 77, 4, 30, "Text"], Cell[342946, 8955, 4938, 127, 83, "Input"], Cell[347887, 9084, 9480, 264, 72, "Text"], Cell[357370, 9350, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[357469, 9356, 59, 1, 46, "Subsection", CellTags->"T1.6.45.1"], Cell[357531, 9359, 132, 3, 26, "Input"], Cell[357666, 9364, 438, 11, 41, "Input"], Cell[358107, 9377, 57, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[358201, 9383, 61, 1, 46, "Subsection", CellTags->"T1.6.46.1"], Cell[358265, 9386, 170, 3, 26, "Input"], Cell[358438, 9391, 444, 11, 41, "Input"], Cell[358885, 9404, 59, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[358981, 9410, 57, 1, 46, "Subsection", CellTags->"T1.6.47.1"], Cell[359041, 9413, 77, 4, 30, "Text"], Cell[359121, 9419, 5780, 139, 100, "Input"], Cell[364904, 9560, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[365003, 9566, 59, 1, 46, "Subsection", CellTags->"T1.6.48.1"], Cell[365065, 9569, 132, 3, 26, "Input"], Cell[365200, 9574, 450, 11, 41, "Input"], Cell[365653, 9587, 57, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[365747, 9593, 61, 1, 46, "Subsection", CellTags->"T1.6.49.1"], Cell[365811, 9596, 170, 3, 26, "Input"], Cell[365984, 9601, 460, 11, 41, "Input"], Cell[366447, 9614, 59, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[366543, 9620, 57, 1, 46, "Subsection", CellTags->"T1.6.50.1"], Cell[366603, 9623, 77, 4, 30, "Text"], Cell[366683, 9629, 12305, 292, 222, "Input"], Cell[378991, 9923, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[379090, 9929, 59, 1, 46, "Subsection", CellTags->"T1.6.51.1"], Cell[379152, 9932, 46, 1, 26, "Input"], Cell[379201, 9935, 426, 11, 41, "Input"], Cell[379630, 9948, 104, 3, 47, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[379771, 9956, 57, 1, 46, "Subsection", CellTags->"T1.6.52.1"], Cell[379831, 9959, 157, 7, 30, "Text"], Cell[379991, 9968, 5078, 127, 116, "Input"], Cell[385072, 10097, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[385171, 10103, 59, 1, 46, "Subsection", CellTags->"T1.6.53.1"], Cell[385233, 10106, 137, 3, 26, "Input"], Cell[385373, 10111, 142, 3, 26, "Input"], Cell[385518, 10116, 57, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[385612, 10122, 61, 1, 46, "Subsection", CellTags->"T1.6.54.1"], Cell[385676, 10125, 162, 3, 26, "Input"], Cell[385841, 10130, 148, 3, 26, "Input"], Cell[385992, 10135, 59, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[386088, 10141, 61, 1, 46, "Subsection", CellTags->"T1.6.55.1"], Cell[386152, 10144, 162, 3, 26, "Input"], Cell[386317, 10149, 148, 3, 26, "Input"], Cell[386468, 10154, 59, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[386564, 10160, 57, 1, 46, "Subsection", CellTags->"T1.6.56.1"], Cell[386624, 10163, 147, 7, 30, "Text"], Cell[386774, 10172, 5563, 141, 100, "Input"], Cell[392340, 10315, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[392439, 10321, 59, 1, 46, "Subsection", CellTags->"T1.6.57.1"], Cell[392501, 10324, 89, 1, 26, "Input"], Cell[392593, 10327, 142, 3, 26, "Input"], Cell[392738, 10332, 57, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[392832, 10338, 57, 1, 46, "Subsection", CellTags->"T1.6.58.1"], Cell[392892, 10341, 138, 6, 30, "Text"], Cell[393033, 10349, 4332, 107, 82, "Input"], Cell[397368, 10458, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[397467, 10464, 59, 1, 46, "Subsection", CellTags->"T1.6.59.1"], Cell[397529, 10467, 97, 2, 26, "Input"], Cell[397629, 10471, 152, 4, 26, "Input"], Cell[397784, 10477, 57, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[397878, 10483, 57, 1, 46, "Subsection", CellTags->"T1.6.60.1"], Cell[397938, 10486, 156, 7, 30, "Text"], Cell[398097, 10495, 4794, 119, 100, "Input"], Cell[402894, 10616, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[402993, 10622, 59, 1, 46, "Subsection", CellTags->"T1.6.61.1"], Cell[403055, 10625, 157, 3, 26, "Input"], Cell[403215, 10630, 185, 4, 41, "Input"], Cell[403403, 10636, 57, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[403497, 10642, 61, 1, 46, "Subsection", CellTags->"T1.6.62.1"], Cell[403561, 10645, 191, 4, 26, "Input"], Cell[403755, 10651, 191, 4, 41, "Input"], Cell[403949, 10657, 59, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[404045, 10663, 61, 1, 46, "Subsection", CellTags->"T1.6.63.1"], Cell[404109, 10666, 208, 4, 26, "Input"], Cell[404320, 10672, 191, 4, 41, "Input"], Cell[404514, 10678, 59, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[404610, 10684, 57, 1, 46, "Subsection", CellTags->"T1.6.64.1"], Cell[404670, 10687, 146, 7, 30, "Text"], Cell[404819, 10696, 10034, 234, 258, "Input"], Cell[414856, 10932, 62, 1, 26, "Input"], Cell[414921, 10935, 50, 1, 26, "Input"], Cell[414974, 10938, 125, 3, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[415136, 10946, 59, 1, 46, "Subsection", CellTags->"T1.6.65.1"], Cell[415198, 10949, 117, 3, 26, "Input"], Cell[415318, 10954, 185, 4, 41, "Input"], Cell[415506, 10960, 57, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[415600, 10966, 61, 1, 46, "Subsection", CellTags->"T1.6.66.1"], Cell[415664, 10969, 148, 3, 26, "Input"], Cell[415815, 10974, 191, 4, 41, "Input"], Cell[416009, 10980, 59, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[416105, 10986, 61, 1, 46, "Subsection", CellTags->"T1.6.67.1"], Cell[416169, 10989, 148, 3, 26, "Input"], Cell[416320, 10994, 191, 4, 41, "Input"], Cell[416514, 11000, 59, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[416610, 11006, 57, 1, 46, "Subsection", CellTags->"T1.6.68.1"], Cell[416670, 11009, 138, 6, 30, "Text"], Cell[416811, 11017, 6599, 156, 153, "Input"], Cell[423413, 11175, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[423512, 11181, 59, 1, 46, "Subsection", CellTags->"T1.6.69.1"], Cell[423574, 11184, 117, 3, 26, "Input"], Cell[423694, 11189, 178, 4, 41, "Input"], Cell[423875, 11195, 57, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[423969, 11201, 57, 1, 46, "Subsection", CellTags->"T1.6.70.1"], Cell[CellGroupData[{ Cell[424051, 11206, 56, 1, 40, "Subsubsection", CellTags->"T1.6.70.1.1"], Cell[424110, 11209, 73, 1, 28, "Input"], Cell[424186, 11212, 184, 4, 28, "Input"], Cell[424373, 11218, 259, 5, 28, "Input"], Cell[424635, 11225, 918, 23, 66, "Input"], Cell[425556, 11250, 188, 3, 63, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[425781, 11258, 56, 1, 40, "Subsubsection", CellTags->"T1.6.70.2.1"], Cell[425840, 11261, 775, 18, 64, "Input"], Cell[426618, 11281, 188, 3, 63, "Input"], Cell[426809, 11286, 47, 1, 26, "Input"], Cell[426859, 11289, 85, 5, 30, "Text"], Cell[426947, 11296, 5136, 131, 166, "Input"], Cell[432086, 11429, 62, 1, 26, "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[432197, 11436, 59, 1, 46, "Subsection", CellTags->"T1.6.71.1"], Cell[432259, 11439, 46, 1, 26, "Input"], Cell[432308, 11442, 149, 4, 41, "Input"], Cell[432460, 11448, 49, 0, 30, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[432546, 11453, 57, 1, 46, "Subsection", CellTags->"T1.6.72.1"], Cell[432606, 11456, 85, 5, 30, "Text"], Cell[432694, 11463, 9048, 206, 278, "Input"], Cell[441745, 11671, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[441844, 11677, 59, 1, 46, "Subsection", CellTags->"T1.6.73.1"], Cell[441906, 11680, 52, 1, 26, "Input"], Cell[441961, 11683, 140, 3, 41, "Input"], Cell[442104, 11688, 49, 0, 30, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[442190, 11693, 57, 1, 46, "Subsection", CellTags->"T1.6.74.1"], Cell[442250, 11696, 77, 4, 30, "Text"], Cell[442330, 11702, 2490, 68, 29, "Input"], Cell[444823, 11772, 66, 1, 26, "Input"], Cell[444892, 11775, 2377, 65, 29, "Input"], Cell[447272, 11842, 66, 1, 26, "Input"], Cell[447341, 11845, 2600, 67, 48, "Input"], Cell[449944, 11914, 66, 1, 26, "Input"], Cell[450013, 11917, 3551, 90, 66, "Input"], Cell[453567, 12009, 66, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[453670, 12015, 60, 1, 46, "Subsection", CellTags->"T1.6.75.1"], Cell[453733, 12018, 77, 1, 26, "Input"], Cell[453813, 12021, 150, 4, 41, "Input"], Cell[453966, 12027, 49, 0, 30, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[454052, 12032, 60, 1, 46, "Subsection", CellTags->"T1.6.76.1"], Cell[454115, 12035, 119, 3, 26, "Input"], Cell[454237, 12040, 176, 4, 41, "Input"], Cell[454416, 12046, 49, 0, 30, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[454502, 12051, 60, 1, 46, "Subsection", CellTags->"T1.6.77.1"], Cell[454565, 12054, 49, 1, 26, "Input"], Cell[454617, 12057, 187, 4, 56, "Input"], Cell[454807, 12063, 49, 0, 30, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[454893, 12068, 60, 1, 46, "Subsection", CellTags->"T1.6.78.1"], Cell[454956, 12071, 77, 1, 26, "Input"], Cell[455036, 12074, 190, 4, 42, "Input"], Cell[455229, 12080, 49, 0, 30, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[455315, 12085, 57, 1, 46, "Subsection", CellTags->"T1.6.79.1"], Cell[455375, 12088, 135, 4, 30, "Text"], Cell[455513, 12094, 66, 1, 26, "Input"], Cell[455582, 12097, 188, 3, 28, "Text"], Cell[455773, 12102, 4719, 112, 63, "Input"], Cell[460495, 12216, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[460594, 12222, 57, 1, 46, "Subsection", CellTags->"T1.6.80.1"], Cell[460654, 12225, 226, 7, 30, "Text"], Cell[460883, 12234, 2102, 56, 48, "Input"], Cell[462988, 12292, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[463087, 12298, 59, 1, 46, "Subsection", CellTags->"T1.6.81.1"], Cell[463149, 12301, 74, 1, 26, "Input"], Cell[463226, 12304, 137, 3, 26, "Input"], Cell[463366, 12309, 49, 0, 30, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[463452, 12314, 57, 1, 46, "Subsection", CellTags->"T1.6.82.1"], Cell[463512, 12317, 77, 4, 30, "Text"], Cell[463592, 12323, 3018, 76, 48, "Input"], Cell[466613, 12401, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[466712, 12407, 59, 1, 46, "Subsection", CellTags->"T1.6.83.1"], Cell[466774, 12410, 74, 1, 26, "Input"], Cell[466851, 12413, 140, 3, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[467028, 12421, 61, 1, 46, "Subsection", CellTags->"T1.6.84.1"], Cell[467092, 12424, 128, 3, 26, "Input"], Cell[467223, 12429, 90, 1, 26, "Input"], Cell[467316, 12432, 179, 4, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[467532, 12441, 61, 1, 46, "Subsection", CellTags->"T1.6.85.1"], Cell[467596, 12444, 175, 4, 26, "Input"], Cell[467774, 12450, 90, 1, 26, "Input"], Cell[467867, 12453, 179, 4, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[468083, 12462, 57, 1, 46, "Subsection", CellTags->"T1.6.86.1"], Cell[468143, 12465, 77, 4, 30, "Text"], Cell[468223, 12471, 2104, 59, 29, "Input"], Cell[470330, 12532, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[470429, 12538, 59, 1, 46, "Subsection", CellTags->"T1.6.87.1"], Cell[470491, 12541, 74, 1, 26, "Input"], Cell[470568, 12544, 151, 4, 41, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[470756, 12553, 57, 1, 46, "Subsection", CellTags->"T1.6.88.1"], Cell[470816, 12556, 77, 4, 30, "Text"], Cell[470896, 12562, 2088, 56, 29, "Input"], Cell[472987, 12620, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[473086, 12626, 59, 1, 46, "Subsection", CellTags->"T1.6.89.1"], Cell[473148, 12629, 46, 1, 26, "Input"], Cell[473197, 12632, 141, 3, 41, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[473375, 12640, 57, 1, 46, "Subsection", CellTags->"T1.6.90.1"], Cell[473435, 12643, 77, 4, 30, "Text"], Cell[473515, 12649, 1286, 36, 29, "Input"], Cell[474804, 12687, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[474903, 12693, 59, 1, 46, "Subsection", CellTags->"T1.6.91.1"], Cell[474965, 12696, 74, 1, 26, "Input"], Cell[475042, 12699, 128, 3, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[475207, 12707, 57, 1, 46, "Subsection", CellTags->"T1.6.92.1"], Cell[475267, 12710, 77, 4, 30, "Text"], Cell[475347, 12716, 1144, 32, 29, "Input"], Cell[476494, 12750, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[476593, 12756, 59, 1, 46, "Subsection", CellTags->"T1.6.93.1"], Cell[476655, 12759, 46, 1, 26, "Input"], Cell[476704, 12762, 130, 3, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[476871, 12770, 57, 1, 46, "Subsection", CellTags->"T1.6.94.1"], Cell[476931, 12773, 112, 2, 28, "Text"], Cell[477046, 12777, 1603, 43, 49, "Text"], Cell[478652, 12822, 2068, 58, 48, "Input"], Cell[480723, 12882, 62, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[480822, 12888, 59, 1, 46, "Subsection", CellTags->"T1.6.95.1"], Cell[480884, 12891, 74, 1, 26, "Input"], Cell[480961, 12894, 137, 3, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[481135, 12902, 61, 1, 46, "Subsection", CellTags->"T1.6.96.1"], Cell[481199, 12905, 128, 3, 26, "Input"], Cell[481330, 12910, 143, 3, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[481510, 12918, 61, 1, 46, "Subsection", CellTags->"T1.6.97.1"], Cell[481574, 12921, 128, 3, 26, "Input"], Cell[481705, 12926, 143, 3, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[481885, 12934, 58, 1, 46, "Subsection", CellTags->"T1.6.98.1"], Cell[481946, 12937, 39, 0, 30, "Text"], Cell[481988, 12939, 2876, 77, 31, "Text"], Cell[484867, 13018, 73, 1, 26, "Text"], Cell[484943, 13021, 3007, 83, 48, "Input"], Cell[487953, 13106, 64, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[488054, 13112, 60, 1, 46, "Subsection", CellTags->"T1.6.99.1"], Cell[488117, 13115, 48, 1, 26, "Input"], Cell[488168, 13118, 154, 3, 26, "Input"], Cell[488325, 13123, 58, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[488420, 13129, 62, 1, 46, "Subsection", CellTags->"T1.6.100.1"], Cell[488485, 13132, 85, 1, 26, "Input"], Cell[488573, 13135, 157, 3, 26, "Input"], Cell[488733, 13140, 59, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[488829, 13146, 62, 1, 46, "Subsection", CellTags->"T1.6.101.1"], Cell[488894, 13149, 118, 3, 26, "Input"], Cell[489015, 13154, 157, 3, 26, "Input"], Cell[489175, 13159, 59, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[489271, 13165, 62, 1, 46, "Subsection", CellTags->"T1.6.102.1"], Cell[489336, 13168, 85, 1, 26, "Input"], Cell[489424, 13171, 157, 3, 26, "Input"], Cell[489584, 13176, 59, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[489680, 13182, 62, 1, 46, "Subsection", CellTags->"T1.6.103.1"], Cell[489745, 13185, 85, 1, 26, "Input"], Cell[489833, 13188, 157, 3, 26, "Input"], Cell[489993, 13193, 59, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[490089, 13199, 62, 1, 46, "Subsection", CellTags->"T1.6.104.1"], Cell[490154, 13202, 118, 3, 26, "Input"], Cell[490275, 13207, 157, 3, 26, "Input"], Cell[490435, 13212, 59, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[490531, 13218, 59, 1, 46, "Subsection", CellTags->"T1.6.105.1"], Cell[490593, 13221, 59, 1, 28, "Text"], Cell[490655, 13224, 145, 3, 31, "Text"], Cell[490803, 13229, 431, 9, 87, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[491271, 13243, 61, 1, 46, "Subsection", CellTags->"T1.6.106.1"], Cell[491335, 13246, 48, 1, 26, "Input"], Cell[491386, 13249, 70, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[491493, 13255, 59, 1, 46, "Subsection", CellTags->"T1.6.107.1"], Cell[491555, 13258, 59, 1, 28, "Text"], Cell[491617, 13261, 145, 3, 31, "Text"], Cell[491765, 13266, 562, 14, 102, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[492364, 13285, 61, 1, 46, "Subsection", CellTags->"T1.6.108.1"], Cell[492428, 13288, 48, 1, 26, "Input"], Cell[492479, 13291, 114, 3, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[492630, 13299, 59, 1, 46, "Subsection", CellTags->"T1.6.109.1"], Cell[492692, 13302, 59, 1, 28, "Text"], Cell[492754, 13305, 145, 3, 31, "Text"], Cell[492902, 13310, 396, 8, 72, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[493335, 13323, 61, 1, 46, "Subsection", CellTags->"T1.6.110.1"], Cell[493399, 13326, 48, 1, 26, "Input"], Cell[493450, 13329, 70, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[493557, 13335, 59, 1, 46, "Subsection", CellTags->"T1.6.111.1"], Cell[493619, 13338, 59, 1, 28, "Text"], Cell[493681, 13341, 293, 6, 56, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[494011, 13352, 61, 1, 46, "Subsection", CellTags->"T1.6.112.1"], Cell[494075, 13355, 48, 1, 26, "Input"], Cell[494126, 13358, 70, 1, 26, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[494233, 13364, 59, 1, 46, "Subsection", CellTags->"T1.6.113.1"], Cell[494295, 13367, 43, 0, 30, "Text"], Cell[494341, 13369, 105, 1, 28, "Text"], Cell[494449, 13372, 6709, 171, 104, "Input"], Cell[501161, 13545, 200, 4, 28, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[501398, 13554, 61, 1, 46, "Subsection", CellTags->"T1.6.114.1"], Cell[501462, 13557, 76, 1, 26, "Input"], Cell[501541, 13560, 422, 10, 41, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[502000, 13575, 61, 1, 46, "Subsection", CellTags->"T1.6.115.1"], Cell[502064, 13578, 692, 29, 372, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[502793, 13612, 61, 1, 46, "Subsection", CellTags->"T1.6.116.1"], Cell[502857, 13615, 696, 29, 372, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[503590, 13649, 62, 1, 46, "Subsection", CellTags->"T1.6.117.1"], Cell[503655, 13652, 1020, 19, 240, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[504712, 13676, 62, 1, 46, "Subsection", CellTags->"T1.6.118.1"], Cell[504777, 13679, 983, 18, 225, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[505797, 13702, 62, 1, 46, "Subsection", CellTags->"T1.6.119.1"], Cell[505862, 13705, 981, 18, 225, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[506880, 13728, 61, 1, 46, "Subsection", CellTags->"T1.6.120.1"], Cell[506944, 13731, 240, 6, 78, "Input"], Cell[507187, 13739, 4682, 85, 136, "Input"], Cell[511872, 13826, 40, 1, 26, "Input"], Cell[511915, 13829, 625, 12, 118, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[512577, 13846, 60, 1, 46, "Subsection", CellTags->"T1.6.121.1"], Cell[512640, 13849, 397, 6, 72, "Input"], Cell[513040, 13857, 428, 7, 72, "Input"], Cell[513471, 13866, 428, 7, 72, "Input"], Cell[513902, 13875, 417, 6, 72, "Input"], Cell[514322, 13883, 220, 14, 185, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[514579, 13902, 61, 1, 46, "Subsection", CellTags->"T1.6.122.1"], Cell[514643, 13905, 274, 5, 56, "Input"], Cell[514920, 13912, 274, 5, 56, "Input"], Cell[515197, 13919, 133, 3, 38, "Input"], Cell[515333, 13924, 262, 4, 56, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[515632, 13933, 60, 1, 46, "Subsection", CellTags->"T1.6.123.1"], Cell[515695, 13936, 183, 3, 41, "Input"], Cell[515881, 13941, 183, 3, 41, "Input"], Cell[516067, 13946, 183, 3, 41, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[516287, 13954, 58, 1, 46, "Subsection", CellTags->"T1.6.124.1"], Cell[516348, 13957, 131, 2, 41, "Input"], Cell[516482, 13961, 131, 2, 41, "Input"], Cell[516616, 13965, 88, 1, 26, "Input"], Cell[516707, 13968, 86, 1, 26, "Input"], Cell[516796, 13971, 89, 1, 26, "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[516934, 13978, 108, 2, 34, "Section", CellTags->"T1.7.1"], Cell[CellGroupData[{ Cell[517067, 13984, 56, 1, 46, "Subsection", CellTags->"T1.7.1.1"], Cell[517126, 13987, 45, 0, 30, "Text"], Cell[517174, 13989, 534, 13, 56, "Input"], Cell[517711, 14004, 145, 3, 41, "Input"], Cell[517859, 14009, 438, 10, 41, "Input"], Cell[518300, 14021, 26, 0, 30, "Text"], Cell[518329, 14023, 899, 18, 292, "Input"], Cell[519231, 14043, 72, 1, 28, "Text"], Cell[519306, 14046, 874, 17, 292, "Input"], Cell[520183, 14065, 82, 1, 26, "Text"], Cell[520268, 14068, 717, 15, 232, "Input"], Cell[520988, 14085, 82, 1, 26, "Text"], Cell[521073, 14088, 738, 15, 212, "Input"], Cell[521814, 14105, 85, 1, 26, "Text"], Cell[521902, 14108, 797, 17, 249, "Input"], Cell[522702, 14127, 37, 0, 30, "Text"], Cell[522742, 14129, 676, 16, 119, "Input"], Cell[523421, 14147, 37, 0, 30, "Text"], Cell[523461, 14149, 676, 16, 119, "Input"], Cell[524140, 14167, 35, 0, 30, "Text"], Cell[524178, 14169, 777, 15, 287, "Input"], Cell[524958, 14186, 226, 7, 92, "Input"], Cell[525187, 14195, 148, 4, 47, "Text"], Cell[525338, 14201, 422, 14, 198, "Input"], Cell[525763, 14217, 422, 14, 198, "Input"], Cell[526188, 14233, 49, 0, 30, "Text"], Cell[526240, 14235, 390, 8, 129, "Input"], Cell[526633, 14245, 49, 0, 30, "Text"], Cell[526685, 14247, 390, 8, 129, "Input"], Cell[527078, 14257, 25, 0, 30, "Text"], Cell[527106, 14259, 212, 4, 56, "Input"], Cell[527321, 14265, 240, 5, 56, "Input"], Cell[527564, 14272, 517, 11, 204, "Input"], Cell[528084, 14285, 1018, 22, 280, "Input"], Cell[529105, 14309, 1018, 22, 280, "Input"], Cell[530126, 14333, 37, 0, 30, "Text"], Cell[530166, 14335, 519, 10, 211, "Input"], Cell[530688, 14347, 279, 6, 56, "Input"], Cell[530970, 14355, 608, 21, 278, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[531615, 14381, 50, 1, 46, "Subsection", CellTags->"T1.7.2.1"], Cell[531668, 14384, 86, 3, 47, "Text"], Cell[531757, 14389, 630, 11, 142, "Input"], Cell[532390, 14402, 191, 3, 41, "Input"], Cell[532584, 14407, 191, 3, 41, "Input"], Cell[532778, 14412, 660, 11, 120, "Input"], Cell[533441, 14425, 163, 2, 41, "Input"], Cell[533607, 14429, 163, 2, 41, "Input"], Cell[533773, 14433, 472, 7, 85, "Input"], Cell[534248, 14442, 164, 2, 41, "Input"], Cell[534415, 14446, 164, 2, 41, "Input"], Cell[534582, 14450, 532, 8, 122, "Input"], Cell[535117, 14460, 543, 8, 114, "Input"], Cell[535663, 14470, 22, 0, 30, "Text"], Cell[535688, 14472, 115, 2, 28, "Input"], Cell[535806, 14476, 88, 1, 26, "Input"], Cell[535897, 14479, 498, 9, 129, "Input"], Cell[536398, 14490, 564, 11, 126, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[536999, 14506, 54, 1, 46, "Subsection", CellTags->"T1.7.3.1"], Cell[537056, 14509, 62, 1, 26, "Input"], Cell[537121, 14512, 1361, 25, 256, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[538519, 14542, 59, 1, 46, "Subsection", CellTags->"T1.7.4.1"], Cell[538581, 14545, 100, 2, 26, "Input"], Cell[538684, 14549, 254, 5, 56, "Input"], Cell[538941, 14556, 7062, 142, 702, "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[546052, 14704, 92, 2, 34, "Section", CellTags->"T1.8.1"], Cell[546147, 14708, 153, 2, 56, "Input"], Cell[546303, 14712, 166, 2, 56, "Input"], Cell[546472, 14716, 3542, 67, 834, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[550051, 14788, 93, 2, 34, "Section", CellTags->"T1.9.1"], Cell[CellGroupData[{ Cell[550169, 14794, 54, 1, 46, "Subsection", CellTags->"T1.9.1.1"], Cell[550226, 14797, 61, 0, 30, "Text"], Cell[550290, 14799, 178, 3, 41, "Input"], Cell[550471, 14804, 65, 1, 26, "Input"], Cell[550539, 14807, 1787, 32, 256, "Input"], Cell[552329, 14841, 53, 1, 26, "Input"], Cell[552385, 14844, 119, 3, 26, "Input"], Cell[552507, 14849, 81, 1, 26, "Input"], Cell[552591, 14852, 135, 2, 41, "Input"], Cell[552729, 14856, 94, 2, 30, "Text"], Cell[552826, 14860, 69, 1, 26, "Input"], Cell[552898, 14863, 54, 1, 26, "Input"], Cell[552955, 14866, 45, 1, 26, "Input"], Cell[553003, 14869, 54, 1, 26, "Input"], Cell[553060, 14872, 44, 1, 26, "Input"], Cell[553107, 14875, 51, 1, 26, "Input"], Cell[553161, 14878, 92, 1, 26, "Input"], Cell[553256, 14881, 84, 1, 41, "Input"], Cell[553343, 14884, 109, 2, 41, "Input"], Cell[553455, 14888, 77, 1, 26, "Input"], Cell[553535, 14891, 181, 3, 41, "Input"], Cell[553719, 14896, 44, 1, 26, "Input"], Cell[553766, 14899, 57, 1, 26, "Input"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[553872, 14906, 95, 2, 34, "Section", CellTags->"T1.10.1"], Cell[553970, 14910, 111, 3, 30, "Text"], Cell[554084, 14915, 1669, 54, 718, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[555790, 14974, 101, 2, 34, "Section", CellTags->"T1.11.1"], Cell[555894, 14978, 46, 1, 26, "Input"], Cell[555943, 14981, 2487, 43, 779, "Input"], Cell[558433, 15026, 87, 2, 32, "Text"], Cell[558523, 15030, 112, 2, 43, "Input"], Cell[558638, 15034, 55, 0, 32, "Text"], Cell[558696, 15036, 134, 3, 43, "Input"], Cell[558833, 15041, 62, 1, 27, "Input"], Cell[558898, 15044, 44, 1, 27, "Input"], Cell[558945, 15047, 48, 1, 27, "Input"], Cell[558996, 15050, 46, 1, 27, "Input"] }, Closed]] }, Open ]] } ] *) (*********************************************************************** End of Mathematica Notebook file. ***********************************************************************)